Lets be honest, thats more or less what competitive gaming is: people sitting on their asses clicking and pushing buttons. The reason why you could get away with saying "I played football" and not with "I played professional League" is mainly because its just not as an impressive. Everyone knows what football is, and how physically taxing it is. Electronic entertainment does not have that luxury to it. As much as people may try to deny it, in the end, playing a video game really just involves you sitting down and pressing buttons(or clicking a mouse or whatever).
As to why ESPN had blacklash for streaming DOTA 2? I don't think its because its a "social stigma." It simply doesn't belong on ESPN. Most people who go on ESPN aren't going there to watch people play video games, they're going there to watch people play football/soccer/baseball/golf or whatever physical activity grabs their fancy. I'm shit at anologies, so forgive me, but its like if I turned to Cartoon Network, and got treated to a Japanese Slice-of-Life anime. You can argue that its technically a cartoon, but its not the sort of thing I'm going to Cartoon Network for. (But lets be fair, who really watches Cartoon Network anymore?)
I've never heard of Froggen by the way, but I think that proves a point that competitive gaming is in a really niche position. I like to play games seriously, but if you asked to name 3 professional Street Fighter players, I couldn't even give you one. Everyone (American) knows who Tom Brady is, because Football is big. Competitive gaming only really matters to very few in comparison.
I'm no good at ending essays, so let me end with a TL;DR
TL;DR: competitive gaming is too different and too niche to really be compared to with athletic sports.
AAI1 and AAI2 are chronologically before Apollo Justice, but they're more or less standalone after Trials and Tribulations, so it doesn't matter when you play them after that point.
Veez got a reaction from ICBMoose in TIAM IV: Guydiana Jones and the Kingdom of the Crystal Cockmongler
Veez got a reaction from John Caveson in Are eSports "real" sports?
Veez got a reaction from Silent in TIAM: General Gaming edition