Overwatch is a class-based team deathmatch arena shooter - the same genre as TF2 and a descendent from Quake. It’s a FPS subgenre and it’s really not that hard to define. Sure, Overwatch borrows some concepts from MOBAs, but the mixture is more like 85-15 than the 50-50 that some people make it out to be.
As for OP’s assertion that ‘A hero shooter isn’t the same as an FPS’, Overwatch is an FPS but different FPS subgenres carry different expectations of what is allowed. For example, respawning mid-round isn’t allowed in ‘tactical’ shooters like Counter-Strike but is expected in team-deathmatch games like TF2.
The same applies to game mechanics - some FPS subgenres are all about realism (you need to lie prone or look down the sights of your gun before you fire, you can only run for a while) and others just let you go full-speed and hip-fire all the time. Both are fine, as long as they fit their genre.
Again, this applies to weapon mechanics - the TF2 pyro’s flamethrower is fine in its’ genre but wouldn’t fly in CS:GO, for example. This is also why complaints about Moira are strange - Moira’s beam is not unique to Overwatch and is in fact nothing out of the ordinary for this genre. People seem to be complaining about one of the staples of the genre: imprecise, low-aim weapons exist to counter high-mobility classes (Scout in TF2, Genji in Overwatch).