First off, what do I mean by "identity"?
Another word to help explain would be "vision". Essentially, what do you want your game to actually be? Obviously in terms of genre and visuals, but also what your mechanics represent, and how your game is balanced. To give a basic example, I'll use Counter-Strike: Global Offensive, or CS:GO. Counter-Strike has a long legacy of being known as a skill-based shooter. You don't unlock new characters with different abilities or unlock different weapons because it would go against what the game stands for; you as a player get better, not your character. This is clearly seen in the games economy system. Each match starts with all players having an equal amount of money. Performing certain actions such as getting kills, winning rounds, or planting bombs earn you more money. You can use what you've earned to purchase better weapons and equipment. What you buy is left entirely up to you. Some weapons are a lot stronger than others, but cost more money, so you have to balance when to spend your cash. Every round you have to decide as a team if you want to spend a little amount of money in order to save up for better equipment, or spend it all for the maximum chance at winning the round.
The rest of CS:GO's design further emphasizes its skill based identity. Head shots do significantly more damage than body shots (1-2 hit kill compared to 4-6), heavily rewarding precise aim. Memorizable spray patterns make spraying worse than shooting slowly and accurately, unless you spend the time to learn each weapons unique spray pattern. With all this, it wouldn't make sense by introducing an unlock system similar to many other shooters, most notably Battlefield and Call of Duty. As I said before, CS:GO bases its design off of the player getting better, not their character. This doesn't make the game better or worse than other shooters, but it was important for the designers to remember this throughout development.
There are two main ways I've seen the vision a game compromised, through out of place mechanics/gameplay systems and incorrectly balancing strategies/characters.
How does your vision affect mechanics?
This is similar to the CS:GO example I gave above, and it's a lot more simple than balancing. A game that very clearly demonstrates out of place mechanics is Mirror's Edge and its reboot, Mirror's Edge: Catalyst.
The original Mirror's Edge is a first-person parkour game, with obviously a focus on movement. One of the reasons the game was talked about was because of its difference between other popular releases. Yes, it had melee combat, it had guns, but you were encouraged not to use these mechanics, and instead focus on moving through the level as fast as possible. To encourage movement even more, there are no forced combat sections in Mirror's Edge, the exception being one boss fight.
Mirror's Edge: Catalyst tried to fix a lot of the problems people had with the first game, most notably the melee combat and gunplay. The solutions implemented were to remove guns, and rework the combat system to allow you to maintain momentum while fighting enemies. On the surface I'm ok with this, even if I liked how the original didn't focus on combat. But the way they showed off their new movement based combat system, was by having multiple arena battles that can only be finished by killing all the enemies. So they mixed combat and movement into one, but then removed the movement aspect by trapping you in with the enemies.
While mechanics and gameplay systems are probably the most common ways a games' vision is compromised, the balancing of a game is also very important.
How does your vision influence balance?
Now this is a topic that I'm very passionate about, as I love fighting games and they typically don't take this into account, or at least it doesn't seem like it. I'm going to focus on fighting games for this section as I feel they are unique when compared to other competitive games. The biggest thing to consider when balancing fighting games is remembering that they're (usually) 1 player versus 1 player. This completely changes the way the game should be viewed. When people talk about "balance" they usually imply that all strategies/characters should be equally viable, but I don't think this applies to fighting games. I'll essentially be arguing for intentionally making certain characters bad.
In other competitive games, like League of Legends, I think it's important to try to make the bad champions better. This is because LoL is 5v5. When you're playing on a team, the last thing you want is for one of your teammates to pick a bad character. Even if they're good with that character, it means they know how to play the game and would still be better suited playing an objectively better character. This encourages players to pick good characters, instead of characters they're interested in. In fighting games, picking a bad character also holds you back, but that's it, there is not 4 other players on your team who your decision also influences. LoL makes this even worse by not allowing 2 players to pick the same champion (in ranked), meaning if you don't pick the best character, the other team will. This difference between the genres isn't why I think bad characters are important in fighting games, but rather why I think bad characters should be made better in team-based games.
As for why bad characters are important in fighting games, it all comes down to play styles. It's obviously important to add variety in a fighting game by having lots of different characters with different play styles/unique mechanics. When balancing all these characters, you have to consider what you want your game to be. An example of a game that failed in this aspect is Street Fighter V. The game received very little balance changes in the first year, as Capcom wanted to wait for the tournament season to be over before changing the game. Some of the strongest characters in that first year were Ryu, Ken, and Chun Li. For the most part, these characters are designed to represent the fundamentals of Street Fighter. They all have decent range on their attacks, one basic, easy to understand projectile, and they don't have any bizarre unique mechanics. These are characters that don't have a specialized play style, they can do everything and deal with anything to a decent degree. These characters are designed so that a player should have a grasp on all aspects of the game (spacing, execution, reactions etc.) to play them well.
If you take a look at what characters were considered bad(or just not great) at the time, you get characters like Laura, Balrog, and Ibuki. These characters are not designed with all the fundamentals in mind, which is ok because it adds diversity in the way characters play. Those 3 characters all have very clear flaws when it comes to the "neutral" game, which is essentially what goes on before someone gets a hit. They struggle to get that first hit, but once they do, they repeatedly put you in situations that make you guess. Are they going to hit you with a low or high attack? Are they going to hit you from the left or right? Are they going to throw you? It's what most people would call a "mixup". For as long as I've played fighting games, people considered Street Fighter the Chess of fighting games, with gameplay designed completely around outsmarting your opponent. Characters based around mixups are extremely annoying to fight against because when you lose to them you aren't being outsmarted, you're just guessing incorrectly.
At the end of last year, Capcom released a major balance patch for SFV, and it made a lot of those fundamental characters worse, and a lot of those mixup characters better. Why? Some people want balance changes like this because they want to see different characters being played, as they got bored of saying the same characters over and over again. I would have no problem with that, but with SFV it meant making the meta of the game completely different from the games identity. People know Street Fighter heavily focuses on the fundamentals of fighting games, and I don't think it's worth compromising that for the sake of "balance".
Why does any of this matter?
Focusing on your games' identity is extremely important, especially for smaller games/studios. Every game has its fan base, some are a lot smaller than others. If your fan base is small, that's fine, but try to think about why they like your game. If you continue to make them happy, they'll actually market your game for you, by posting online or by word of mouth. This is extremely important for indie studios, as they don't always have the money for a large marketing campaign. If you release a patch or a follow up game that messes with the parts your fans are so attached to, they'll feel like they aren't being listened to. Unhappy fans are not going to help spread the word about your game.