Don't you worry.
First of all, the leaks and hypothetical comments made by Phil Spencer tell us the game will have the classic multiplayer. Spencer said that if H2A existed, its multiplayer would have to do a better job than that of CEA's. By using H4's engine, they would be doing the same thing again.
Secondly, using H4's engine would simply be impractical. 343i would have to completely rebuild the multiplayer maps in H4's engine, which is obviously harder than just reskinning things. Additionally, H4 would have to be ported over to the X1 (which might not be too hard) but also would need to have 60FPS, assuming 343i wasn't lying. Correct me if I'm wrong, but I'm pretty sure that would involve a complete engine overhaul, which in my mind seems like unnecessary effort when there are clearly easier alternatives. Why work harder when you're just gonna piss everyone off?
So, instead, they can just port H2 Vista over, which already includes 60FPS and dedicated server support. Because the PC's and X1's hardware are similar, the porting process is not difficult, at least compared to porting a 360 game over to X1. All of the maps and whatnot are already there. All that would need to be done is to reskin the maps, which is not only possible, but can be done by amateurs using the mod tools that [i]came with the game[/i].
Or am I missing something?
EDIT: Helpful links
[url=http://www.ign.com/articles/2014/03/27/xbox-boss-a-halo-2-remake-would-have-to-nail-multiplayer]Phil Spencer on H2A multiplayer[/url]
[url=http://www.neogaf.com/forum/showthread.php?t=760013]Neogaf leak[/url]
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They wouldn't use the Halo 4 engine because they have a new one for halo 5