I don't know if the Atari Lynx counts as non-major. Anything from Atari should probably count as major, the thing supposedly sold 2 million units, but I can't remember the last time I've seen anyone mention it and that's still less than 2% of the Game Boy's 110m+.

I got the original model as a hand-me-down towards the end of the 90s and I wasn't super fond of it. The thing looks and feels like a brick and ate batteries for breakfast, the internet says 5 hour battery life but I remember getting like 2. The "left-hand mode" is a cool concept but putting two pairs of A/B buttons on the device feels like something they could've done better. It had color, a couple of arcade ports were really great games and there was Chip's Challenge, but younger me got exhausted just using the damn thing.