Do you know the game I play? I think that it's quite fun.

Find the rules that bind it, and you just might find the one.

This puzzle's for lovers once kissing - and a missing thing used for things missing.

This looks like a stretch, but my guess is

the letter X.

Do you know the game I play? I think that it's quite fun.

It could be Tic-Tac-Toe/naughts and crosses (credits to jsm who validated my idea)

Find the rules that bind it, and you just might find the one.

In this puzzle, the only missing letter is the "X".

This puzzle's for lovers once kissing - and a missing thing used for things missing.

Lovers once kissing = "ex", which sounds like "X", and x as the variable to be uncovered in maths expressions.

Title:

It refers to "xoxo" placed at the end of letters or text messages, which means "hugs and kisses". "Read my lips" means "read the x as a kiss". (credits to tyobrien)

• Correct answer. The reasoning is close but not quite there. What did I mean with the title and the game? May 25, 2018 at 12:50
• ...by the way, if somebody has a guess for the title or the game, please help me :D May 25, 2018 at 15:33
• You know the meaning of the characters xoxo...? May 26, 2018 at 0:43
• @LinuxBlanket The answer I was looking for might not be common knowledge. A “lipogram” is a form of writing which avoids certain letters, mainly just for fun. The title and the first two lines describe the concept. “Read my lips” is a play on words, “lip-“ is to leave out, so the title suggests that you “read what I have left out”. May 26, 2018 at 21:07
• @kedarguru ah sure, a lipogram! I know it, mainly from Queneau's work :) now I feel quite dumb for not thinking about it, it was self-evident May 26, 2018 at 21:10

Not an answer, but I noticed a pattern:

While prononcing the lines, the lips touch exactly twice every line: