If there is a game that is purely mathematical and does not rely on decision making then artificial intelligence can dominate. If the game needs decisions like in chess, the machine will beat most people but it s stil possible for some humans to win. Most people are not smart enough to defeat AI.
Regardless of how much time is spent on making an "invincible" AI, there is no such thing as perfection. An AI is made by humans - because humans are prone to error, AIs are also prone to the latter. The only way to create an invincible AI would to be, of course give the AI an "invincibility cheat" .
AI usually has some kind of limitation that ends its function, so I don't believe a robot can't be defeated by the game it belongs to. That sounds like pure science fiction. And if it ever could be done it would look badly upon the inventor. People should not let their inventions get out of control, especially in the case of AI.
No, it is not possible to create an Al that can't be defeated in any type of game, because human intelligence is always superior to that of a machine. Artificial Intelligence can only do what it has been trained and programmed to do. That is, AI is no better than the human that made it. However, a human has the ability to reason, and that is always superior.
It is possible to create an artificial intelligence that cannot be defeated at tic tac toe. It is NOT possible to create an artificial intelligence that cannot be defeated at Pictionary or Win, Lose, or Draw for example. There will always be a human element in games, at least games that aren't rudimentary.