Personally, I think that as long as you've got a full manual manipulation of the bolt, it's a pump in my book. That counts out the assisted pumps and SHO types. I'm not a huge believer in the e-trigger for a pump either, although I did get to try out an amazing Angel framed, MQ2'd T2 once. Pretty incredible gun. But once you get into that kind of thing, it's almost screwing with the "spirit of the idea".
As for the tournament series, no idea, I've never gotten to that point where I thought it was a good idea to jump into that.