(Fan game) Sonic the Hedgehog - Nintendo Edition (Early WIP)

[Vipershark]

The Gameboy uses square waves but not only square waves.
It's also got a triangle wave, noise generator, and DCPM but as far as I know the Game Gear uses square waves only so all of its music (the sonic games in particular) has this distinct "doot doot doot" sound to them because everything is just squares all the time.
I think most gameboy games generally had the main melody and accompaniment be squares while the bass and percussion were triangles and noise/DCPM respectively (but that doesn't apply to every game of course)

You'd probably be best asking Gorsal or someone more familiar with chiptunes how to give it the most authentic sound (particularly if this would have been a first party Nintendo collaboration, the music would have been really good).

On the intro in your OP for example, when the title screen comes up the first three beats you use an ugly buzzing sound when noise or DCPM would have worked much better.