Well, Tyrannosauroidea is the superfamily name within Coelurosauria, so technically it encompasses everything from Proceratosaurus to Tyrannosaurus. The group only has two subdivisions, Proceratosauridae and Tyrannosauridae, but has a large nexus of animals which don't fit into either of those (they're more basal than tyrannosaurids, and typically more derived than proceratosaurids). There's a lot of uncertainty around the early members of the family, some researchers don't consider proceratosaurids to be a valid group at all.
Personally though, if I'm talking about a 'tyrannosauroid', I'm generally talking about something from the family that's more basal than a tyrannosaurid. There's a pretty clear divide - the earlier members of the group are mostly small, three-fingered sprinters, whereas pretty much all the tyrannosaurids are huge and bulky with two functional fingers.
Tooth fossils can be very misleading, as tooth shape can be similar through convergent evolution rather than a taxonomic relationship (I'm guessing you know that already). It's also incredibly rare for a tooth find to later be associated with a full animal (which gives you some idea of what a vast number of species there must have been). With that said, in this case, the teeth show a number of evolved traits also seen in Xiongguanlong's, and also occurred contemporaneously, so it'd be one hell of a coincidence if they weren't closely related.
Anyway, in my opinion the 20Ma gap between Siats and Lythronax is caused by the incomplete fossil record rather than a lack of the niche being filled. There should be a series of 500-1500kg tyrannosauroids with diminishing arms, heavier builds and deepening skulls lurking somewhere in the deposits of that period.