For you, it's competitive. You're not going to convince me that "league is competitive" is an axiom.
Btw, before you try to interpret it as such, I'm not giving my opinion on league's competitive nature, nor what does competition mean to me. I'm merely commenting on your rigid "you have to do things my way" outlook instead of working with your teammates and their mentality which is by nature of humanity going to be varied. There'll be no guarantee that they'll jive up in a random assortment of 5 people.
You mention that 'You can dip around with your 5 man all you want'. The reverse is also true. Whenever you want to force your ideology on someone else, you always have the option to 5 man with like minded people. Until it is in the ToS that you MUST treat the game a certain way, it'll just be your opinion, nothing more and nothing less. EDIT: There is always the chance that you are so ragey, commanding, and generally unfun to play alongside that you're not going to get a 5 man group (at least for long) which then you're just going to be stuck.
"It's just a game" is not synonymous with "I'm not trying". I have yet to see someone who says that suggest that they're the same. If you think it is, then that's your opinion and it is fine if you want to interpret it that way. Just take it to the pro scene or 5 mans where it isn't. It's not a reason to flame people.
Personally, I think it's a far bigger problem that people feel justified in being angry and venting your frustration at someone else because they don't share your same ideology.
If you want to victimize everything in your life where it's 'you are wasting my time by not being as serious as I am', that's another life choice I guess. They have a place for people like that and I believe it's usually called "Anger Management Classes" because the tendency that I see is that you are much angrier in your life.
As to your "Getting into games with people like that puts anyone on edge and causes such a toxic form of mistrust it's disgusting." comment, that can be the case, but it's a personal life outlook that I do not share because it's what causes the toxicity itself... not that the situation itself is toxic. A lot of the times people bring a lot of this 'toxicity' on themselves without the ability to introspect and they are probably the cause... and not the symptom.