Ah, yes, proper Game Mode stories - my favourite kind of story on CHYOA.
MidbossMan has already taken half of my recommendations, but I'll doubly echo the awesome Becoming a Warrior! and also mention
Goodbye Girls again, which is deserving of far more attention than it currently gets. Seriously, the level of thought that has gone into both of these is amazing. Plus, they're both loaded with content and still receiving updates.
I'll also recommend a new story,
The Necromancer and the Wandering Princess. It's only a few days old so it's difficult to gauge how much it's going to end up using Game Mode, but between the concept and the writing quality, it seems extremely promising. I can at least assure you it's not one of those "dump five chapters and run" stories - it's being updated as I write these words.
Whispers of Madness is a dungeon crawl style story that is also highly underappreciated. I haven't read too far deep, but what I have is great.
Speaking of dungeon crawls, I suppose I'll mention my own
Darkest Challenges. I'm not sure it's the same quality as the other stories mentioned here, since it's not really story-driven, but if you've ever played DnD and thought about how great it would be to fuck all the (humanoid) monsters, there you go. It's not too far from being finished, which I'm excited about.