Any idea why the NFLPA went straight for a Preliminary Injunction instead of a TRO like in Texas?
There are all sorts of tactical reasons that come into play so this is somewhat speculative. But recall that they moved for the TRO in Texas before Henderson had issued his ruling and without clarity on the timing of when that ruling would come down.
The primary difference between a TRO and a PI lies in the timing: a TRO can be issued by the court on the application of the moving party and without any hearing or submissions by the other party. That's what Elliot needed in Texas because there was a real threat that Henderson would issue his ruling on September 9, leaving no time for a hearing before the first game on September 10.
Currently, Elliot has the benefit of the stay pending hearing of the motion for the PI (which is effectively the equivalent of a TRO issued without a hearing) so he's not faced with the same exigent circumstances. If, instead, he could somehow be exposed to irreparable damage before even getting to the hearing of the motion for the PI, the NFLPA would presumably have moved for a TRO instead.