I think it looks quite nice, especially in HDR, although you can't see it in screenshots. They haven't taken the green away, just applied it in subtler and more dynamic ways.
The Matrix footage in that video is messed up, taken from the remastered blu-rays where they somehow screwed up with overblown whites and odd color timing when they toned it down from HDR to SDR.
Anyway, the 1999 DVD had this brown-ish pass. The 2008 blu-rays had a green-ish pass. And the UHD master for me just has richer look to it.
I never liked the overbearing green in the previous master, it's just really distracting.