To clarify when I said this kind of nipping is both play and dominance.
It’s play to the extent that no he isn’t angry or actually trying to kill you.
But like a lot of games, it is about establishing dominance. Young geldings are a lot like 12 year old boys. Left unsupervised 12 year old boys will often be wrestling and shoving each other around until the pecking order is sorted out.
So yes it’s a game and yes your horse is keeping score. Nip slap nip means he’s still scoring points in his mind.
If you are fast enough to intervene before he actually lands a nip he has not scored a point and it’s a lot less fun. And if you make him move his feet back and give way you have asserted yourself like another horse would.
When you do that, let him stand at a distance from you until he drops his head or looks away, and then let him come back to you.
Obviously you need to gauge the right level of response to his energy level and you need to have precise timing.
Also I would of course only recommend this with a horse who is already tame and unafraid and who wants to be with you. I wouldn’t send a horse away like this if it was still nervous of people or likely to bolt or spook or rear.
It’s for the pushy confident ones.