If you're able to read and understand the written word, you're literate.
If you're able to count and understand mathematical concepts, you're numerate.
If you're able to play games and understand essential game tropes/concepts/mechanics, you're...?
Example: John could pick up and play any game without much difficulty, because he was very (game literate).
I would think the technical latin-derived equivalent would be approximately ludate, from ludus (game), which would probably be bastardized into luderate, similar to the way we do words with -aholic from alcohol, which is etymologically incoherent.
Having said all that, the words I've suggested above don't seem to exist. Is there anything else that would fit this definition?