Etymology – Why is it “On *the* One Hand”?

This is what the Oxford Online dict says

play on: exploit (a weak or vulnerable point in someone): he played on his opponent’s nerves
play with: treat inconsiderately for one’s own amusement: she likes to play with people’s emotions

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:

Note that curl up is a phrasal verb, and means to curl tightly (or fairly tightly). ODO does not make the distinction clear, and OED only mentions it in passing:

curl v
3 a. To bend, twist, or coil up into a spiral or incurved shape; to make curls or undulations upon (a surface); to ripple (water). Often with up.

coil v
3 c. to coil up  : to twist into a fixed or constrained position.

"Curled up his fingers" is not quite the same as "curled his fingers up": in the latter, the fingers end up pointing upward; in the former, they simply end up curled. Compare "curled his fingers down".