CS:GO and TF2 are huge on PC but aren't nearly as big on 360.
Difference is Minecraft is a game that's accessible to anyone and everyone with a very low learning curve, it's like the textbook definition of pick up and play. You don't need to invest any time into learning how to play in order to get enjoyment out of it. Old folks, parents who only have a few minutes of gaming time available, it's pick up and play and have fun by yourself or with family/friends/kids. LoL is quite literally the complete opposite, it has an insane learning curve, so you're not going to go into LoL "pwning n00bs" you will be getting your asskicked on the regular until you start learning all the heroes, their skills, runes, etc. Even then you're not guaranteed to win. LoL is also competitive MP only. There is no story mode, there is no "relax with family and friends" mode. You have to participate in the community in some form in order to advance. Want new heroes? compete, want new items? compete, want new equipment? compete. But at the same time it's a MOBA so there isn't this exploration/chill/crafting/metagame type component like a MMO. For instance COD is wildly popular, because it's capable of being competitive but at the same time it's pick up and play and has a low learning curve. You can never have played CoD but move the sticks around and squeeze the triggers and you've pretty much learned all of the basics of CoD so you can still have fun. That doesn't really exist in LoL
Accessibility is the name of the game, and it's something Minecraft does better than...well a shitload of games. The argument has never been will LoL on Xbox work. The argument is thinking LoL will be just as huge as Minecraft is vastly oversimplifying why Minecraft is popular in the first place. Minecraft wouldn't be anywhere near as big on 360 if it had a barrier of entry similar to LoL.