So I have been playing Moba's since 2006, I started out with OG Dota moved to HoN for a while switched back to Dota 2 when the beta started, spent a little over a year playing LoL before moving back to Dota 2, and during that time every time I am asked to explain what it is I find myself saying something along the lines of "its a mix of hockey, chess, and football all played much faster". Yes I get that look you have on your face right now every time I say it as well.
I try to avoid saying something like "Oh its like an RTS but you only get 1 character to control" because saying its like an RTS puts some assumptions in your mind that are 99% false. And while by the dictionary definition of a "game" yes Dota and LoL are games, so is football and people dont consider it a game they consider it a sport.
When you dig into the deep strategy of ether of them (or Meta if your being a Moba snob), I think the comparison to something like football or hockey is a much more accurate assessment of what a Moba is, at any given time there are hundreds of things going on and you may not be able to keep track of them (again nearly 9 years of playing them and I still miss things), but much like football or hockey your not thinking about why that guy getting blown up happened and how it was set up by the play that preceded it, your just marveling in the moment of "MAN THAT GUY GOT FUCKED UP".
This isn't meant as an argument that "esports are real sports" or anything like that, I just have spent a lot of time thinking about this and wanted to get other peoples opinions on the subject. Calling them games and lumping them in with what the traditional concept of a game is just seems a little dismissive to me.