I think the problem some users are having is the wording, because the Halo footage shown looks like a PC/Series version and not like a Xbox One game. The last gen console isn't powerful enough to show Halo at that quality. I know what you mean with your wording, but let me show you why the wording is a bit problematic.
The Witcher 3 came out in 2014 and was despite the downgrade uproar one of the best looking games at the time. The game was visually (and quite literally) a current gen game at the time. If someone would've said back in the day that it's a mobile/handheld game, she/he would probably get called a troll or receive criticism.
With Steam Deck on the horizon someone could also call GoW, Horizon, Death Stranding, FH5, Halo, Gears .... and much more mobile/handheld games. If that person uses your logic imo. That's at least my interpretation and please do not take this personally. Let me take FH5 as an example, because most people praise the graphics. There are two issues with calling a game like FH5 a handheld game, despite this being true.
- Saying something like "XY is a last gen, handheld, ... game" always (imo) has a negative ring to it. Even if that's not the intent.
- It's not entirely correct, because games are scalable and the Series X version of FH5 wouldn't run on any handheld or last gen console.
So back to Halo. What you said isn't wrong, since Halo Infinite is (also) a Xbox One game. However and there is the distinction imo, what was shown yesterday isn't possible on Xbox One. So was that version a Xbox One game? Not really.
I wasn't sure wether I should post this, because it's kinda weird to explain and I understood what you meant when saying Halo is a Xbox One game. Having that said I wanted to explain why the wording can be controversial or at least result in some people pushing back.