The GBA could definitely do a real 3D engine but it wouldn't look very good at the low resolution anyway. I remember a demo from back in the day of a Quake-like 3D engine on the GBA but it really didn't look good.
For the DS, note that he seems to be targeting the original DS (e.g. not DSi OR 3DS). I remember there being some slightly better stuff but not significantly better than what he made.
I just ran the DS version on my DS lite, it looks pretty good - definitely comparable to games on the system, and the models seems more detailed then most of what you see on the system. The screenshots just make it look horrible because it's a fairly low-res screen, when you blow it up that big it looks a lot worse then you'd expect. The monkey shadow is definitely iffy looking, but I don't think any games ever did 3D shadows that detailed - there's probably a reason for that. It is worth keeping in mind that the original DS is weak (especial 3D wise), but it's not really that bad considering the low resolution it has to render for. That low resolution is the main reason why it looks so bad in the screenshot though.
The GBA version also looks pretty good on my DS lite (compared to games on the system). You can't rotate the camera though, so the dragon doesn't rotate. The monkey-head rotates on it's own though and looks pretty good. You're right that there are a few games that do 3D on the GBA, but I can't imagine it's fun coding wise since it the hardware support is basically zero in that regard. But there are some weird ones out there - Banjo Pilot comes to mind, which is a weird mode-7 3Dish flying game. Not exactly a great game, but pretty cool to see. Even with that game though, they have to sacrifice basically all terrain to be able to render the other characters at a decent speed IIRC, so the entire game is just flat.
And if you want to get really obscure, there is Faceball 2000 on the GB, which is a "FPS" and is 3D (And runs at like 15 FPS IIRC). There's no way you could render this scene on it though besides just pre-rendered sprites like was done with the GBA.
For the DS, note that he seems to be targeting the original DS (e.g. not DSi OR 3DS). I remember there being some slightly better stuff but not significantly better than what he made.