Early I agree with however it tends to end slightly after laning phases so 10min is best estimation, and it emphasizes when players don't really have any core item or max rank skill yet. I don't agree that not surrendering is a feature of early game because by the 10 minute mark you should already have enough strength to start teamfights or begin split pushing if needed.
Mid game usually starts around ten minutes because that's when you probably have your first core item/max ranked skill then ready to open more options such as teamfight/splitting etc.
Late game tends to be past 25min because that's when you mostly see where you excel and decide whether or not you'll continue working with your team to victory (Most of your core items built and skills leveled)
Endgame which a lot of people don't talk about anymore is when you finished leveling and buying core items which should be around the 40min mark.
TL;DR: Most of the reason why mid game is pushed so early is due to how the game's flow was changed anyways making games faster pace. Still a shame riot hasn't fixed death timers to reflect it though.