Yeah, it's a little weird. If you used it, "Okay, I will mark your words" is better, and it is a slightly playful use of language. More commonly I think I would say "Okay, I'll hold you to that" You could ask "Can I quote you on that?", or simply note "I'll remember that." You could use "I will write that down." Or you might just repeat what they said in some form, to yourself, out loud.. "The man says he'll beat me at Counter Strike..."
The reason I say it is a little playful is that it is an idiom and we normally only encounter it when the speaker is promising what he says will turn out to be true.
It is a dramatic sounding way to emphasize something. A warning, often, or a brag. The word "mark" is intended as "make a note of".