Beware, that's too tight! (See here) I'll also put in a vote for 'lost one spacer'. You need the stem cap to be tightening down on spacer, not on steerer. With loose stem bolts, tighten down the cap just until the play goes away (not sure how to tell if there's play if the stem is not tight yet), then you can crank down on the stem bolts, and once the stem is securely holding down the spacers, you don't even need the cap in there (except keep it on, in an accident an open steerer tube could core you like an apple)

Another possibility related fact: a newly-pressed headset can be nice and tight at first, even if it is not pressed in fully, but as the bike is ridden, the weight will eventually press the headset (and fork race crown) home and leave some slop, so a headset adjustment would be in order. But yours doesn't seem to have happened due to time, but to taking it apart and putting it back together. But, you may consider making yourself a ghetto headset press (bigass bolt, nut and stack of washers), taking the steerer out altogether, and giving the headset cups a squeeze in the headtube to make sure they're fully seated.

Sometimes purists will insist on refacing new headtubes, which I guess means turning a perfectly round, perfect diameter circle in the inside top and bottom of the headtube so the headset will press in perfectly, I wonder if it's possible that your headtube was not perfect and should have been faced? My new CC frame didn't seem to have this issue, I don't know how common it really is.