Like others have said “I play on the guitar” is unnatural by itself. You can say something close though. “I play this song on the guitar” or “I play it on the guitar” work as long as the context is clear.

No, "I play (the) guitar" means you know how to make music on the guitar instrument. "I play on the guitar" means that you are making merriment while physically located on the guitar instrument, not impossible, but unlikely.

Thank you Chris and John. Я играю на гитаре(Russian). Word by word translation(I play on the guitar)

No you usually play in the street or on a football/soccer field;for football/soccer. for other area where you may play it could be "at"

I play on the guitar is unnatural.