No, the two phrases are not interchangeable. “He is cheating at the UNO game” implies that he is using dishonest tactics or breaking the rules to gain an advantage in the game. On the other hand, “He is cheating on the UNO game” suggests that he is being unfaithful to the game, possibly playing a different game or not following the rules properly. As for your question about cheating on a test at school, yes, you can say “She cheated on the test at school.” This means that she used dishonest methods to gain an unfair advantage in the test. I hope i understood what you meant! If you need any more help fell free to message me!

Sensible things to say: He cheats at Uno. He’s cheating at Uno. He’s cheating at Uno over there. He’s cheating. ‘the Uno game’ is a strange thing to say but not necessarily wrong if there is a specific game of Uno going on which has been referenced. It’s a little ambiguous because it sounds like a simple reference to a place. E.g. I’m sitting over there at the Uno game. A test by default is a piece of paper with questions written ON it. So you answer questions on the test. You cheat on the test. But honestly you are wasting your time worrying about prepositions if you say things like ‘Are they have diferente meanings?’

To you an answer with confidence I would need to know what the "UNO game" means. There do exist a few contexts where the words are interchangeable. For example, you could say "The political party is cheating at vote counting" or "The political party is cheating on vote counting". Normally, they do not mean the same.

The phrase “to cheat ON” can be used either - in regard to a test, quiz, exam: “She cheated on the midterm, and still only got a D”, or - to talk about someone being unfaithful to somone else: “She cheated on him, so he broke up with her.” You wouldn’t really say that someone cheated on someTHING (in terms of being unfaithful) unless you were trying to be funny or poetic. As far as “to cheat AT” goes, you would simply say, “He is cheating at Uno” or “…at tennis” or “…at backgammon”; no need to add “the game” as that is already implied.

I think in this context it is more common to hear "He's cheating in the UNO game" or often "Hes cheating" is sufficient. When I hear people claiming someone is cheating in a video game its usually the word "in" rather than "at" or "on".