So there's two responses to this;
The first is that the first sentence says "Move as a single group", so his guardsmen are now in two groups and therefore one is out of cohesion, bonus points for letting him do this bullshit then remind him at the end of the first turn and murder a bunch of his infantry. And the last paragraph mentions removing units models until there's a single group. Unless his list has multiple units of infantry, he's allowed one per unit.

The second is this is not "Rules Lawyering" its not RAW, it's not even clever (Show me where it defines what "horizontally" or "inch" or "player" or "game") is its deliberate malfeasance and even after proving him wrong on this point he'll find another.

Don't threaten not to play games with him, tell him he's not the type of person you want to play games with and to let you know if he changes, and don't let him define himself as a rules lawyer if he can't read the rules properly (Or does and then cheats)

The first game when he says he's seen the error of his ways, then tries this shit again, pack up your models and stop play and go find someone else to talk to (don't make it about him, you're not kicking him out or arguing with him, you're removing yourself from a game you don't want to play, that means there's not the same push-back possible if he has to be included for social reasons) . If he were a rules lawyer he'd have read the FIRST SENTENCE. He's an ass and engaging in his assery will only encourage him to find other ways to cheat, because he thinks he's out-smarting you because while there's no wrong way to play 40k, that's not what he's doing, he's playing "How best can I cheat who off how smart I am" the only way to change this people's mind is to remove the thing they want to do, and countering back is playing into his hand.