Acording to riot, Xerath is an assassin

That is using the old classification system. Back then anything with burst meant you were an assassin. Malzahar is supposedly classed as one.

Well, the fucking damage is there. Artillery assassin, nuff said.

That's the result of the old class system where they had primary and secondary. Xerath (and many others) were secondary assassin because of their damage output.

Honestly, Riot really needs to update their info page with the subclass system on all the champions.

Tristana is also classed as Assassin.

So much damage everyone is an assassin, wouldnt be surprised if a janna 100-20% me with her 2 damage spells lol.