S14 hubs might have play
if they are not torqued to spec
But that does look like an unusual amount of play... Are you sure you didn't break anything on the crowns? Did you install the crowns the same way the came out?
I wouldn't even think about running them without grease.....
I regreased my s14 front hubs but couldn't get the shield thing in the back of the hubs to pop back on completely... I can press it down no problem but it just pops back up even after a good torquing... Did you have this problem?
Edit -
Just checked my front hubs and they do have some play like in your video. Definitely get some wheel bearing grease in there.
Also took a pic of "shield" I was talking about. I know they didn't have this gap before I took them apart and the shields kinda popped out of place when I was taking them apart.... I was expecting them to pop back into place but now they are just kinda sitting there.
