I find this expression strange because it’s clearly widely used, but seems sort of “unofficial”, the “official” version, meaning the one described in dictionaries and grammar books, being playing games with, not on.
Both expressions seem to be current and valid, according to Google Books. I’m just not entirely clear on the context and the usage.
My understanding is that playing games with implies some sort of tricky, mischievous behavior, which may or may not be intentionally malicious, like office politics or standing someone up on a date (“Jane didn’t show up…again. Is she playing games with me?”), while playing games on implies a form of studied deception. (“The ad said that the comic book was in mint condition but there are barely noticeable tears… are they trying to play a game on me?”)
This is what the Oxford Online dict says
And another reference from there shows us that to play games on someone does imply some sort of trick which can be (or not) malicious (technically). But its mostly used in a non-positive sense.
So to ans your question, both play game on and play game with can suggest the malicious nature, depending on what context its being used in. E.g:
“Quit playing games (with me) and come to the point man!”
“He is playing a game on her to like him” -Studied deception
“He will never marry her! He is just playing games with her (for sex)” – suggesting studied deception again.
play games on is less commonly used, and even lesser commonly used in British Eng compared to US, as seen in the Google Ngrams below: