My answer is that it depends on how they contradict the game.
The way I tend to contradict the games in my own fanfiction is make much more usage of the environment around the battle, allowing for certain moves to last beyond the turn they originally took place (for example, an Earthquake causing the ground to vibrate for a decent amount of the battle rather then only for a moment), act differently to how they are programmed in-game if the scenario calls for it (for example, a Metal Claw being used to parry a Steel Wing instead of attacking the opponent), and overall have more creativity with the way the battle plays out so that they remain interesting. This sort of contradiction seems alright to me - it's how a Pokemon battle could play out in real life when moves aren't restricted to a single function, Pokemon can use two moves in one turn if the opponent is slow enough and the Pokemon can utilise the environment around them to their advantage.
The way I don't like to contradict the games can be summarised with a blatant example - Thunder Armour. The sort of contradiction shown in the Ash vs Tate and Liza battle blatantly goes against another rule the anime has already established - weaknesses against particular types. If the anime were to not contradict themselves in this scene, that bird would've been freaking obliterated. Times when what happens in the anime doesn't even make sense in real life are the times when I despise the contradiction.
Basically, if what happens in the anime could happen in real life if Pokemon were to exist, then I'm cool with it. If it defies every single law of physics possible even with the concept of Pokemon existing in the real world, then I'm not cool with it.