I don't actually play League of Legends, but as a parent myself I can toss in my two cents from that perspective:
Overall I feel I understand the gist of the open letter. I'm sure if you're playing a match online and have already invested a degree of time into it (as a parent, most days I'm lucky even to get half an hour of gaming in) having a young team-mate pulled from the game by a parent who doesn't really understand what their child is doing or what impact that has on other people would certainly be frustrating. In that regard, I can get behind an attempt to educate parents about how the game they're allowing their children to play works.
I'm a long-time gamer. At the moment my son is only 3 years old, so we don't play a lot of videogames; but I still try to make it a point to know what games we're playing together and make appropriate choices. He may really want to play Lego Batman 3 right before we have to go to day-care, but if we don't have enough time to get through the story mission he wants to play, then we're just not going to start it.
I think what's going to irk a lot of parents (especially non-gamers) is that this does seem to be coming from someone who doesn't have kids of their own. And one thing parents universally tire of very quickly is parenting advice from people who just - to be frank - don't know what they're talking about.
I think it's perfectly reasonable to want parents to understand what sort of game they are allowing their kids to play. And if it's an online game (where you can't just pause the game come dinner time and pick up later on) to have some understanding of the time commitment involved - that their child is playing with other real people, and that joining a match is an implicit agreement to finish the game, barring unforeseen circumstances.
I would never allow my son to start an online game ten minutes before dinner or another pending obligation - if he were to want to play something like that, we'd need to allot an appropriate amount of time in the day's schedule to allow for that. In that regard I don't find anything untoward about the open letter - that just sounds like reasonable and responsible parenting, and having some idea of what you're child is doing with their free time.
Where I would disagree is the hypothetical situation toward the end of the letter wherein he had started a match right before dinner or bedtime even after I'd said he couldn't. Sorry, but that kid's going to get his computer turned off - I might let him briefly apologize to his team-mates before quitting, but there's no situation I can imagine where I'd allow my child to continue an activity like that after I'd said he couldn't - regardless of whether I later grounded him or suspended his gaming privileges.
In short - absolutely I agree that the proper and responsible thing to do as a parent is to be aware of the nature of the game your child is playing, and to properly allocate time for that. I could even see waiting on dinner for fifteen minutes or so if a match was running a bit long (again though, I'm a gamer as well.) That's just common courtesy. I think it would be irresponsible to allow my child to start up matches with no regard to how that fit into the day's schedule, and would take little effort on my part to help him find time to play at appropriate times of the day. I think it's understandable that by joining an online match, you're implicitly agreeing to certain time investment for all involved.
But if my son's misbehaving and starting up a match after I'd told him not to? Then that's his fault - it's on him that he'd be letting down his team-mates by starting a match he knew he wouldn't be able to finish or at a time he wasn't supposed to be playing it. I wouldn't reward him by allowing him to finish the match - just as if he'd run off to go play football down the street with his friends after I'd said he couldn't, I'd really have little choice but to hunt him down and drag him back home - kicking and screaming - even if that meant his "team" lost the game.
