Makaqu should be ported to the Dingoo A320 handheld.
I’ve recently got one, and it’s pretty good. Also, this handheld has no hardware acceleration, which leaves a lot of room for good software-based renderers to shine in it. It also doesn’t support any kind of networking (except through an USB cable connected to a computer, which kinda defeats the point of playing on a handheld), and it doesn’t support external controllers either, so single-player gaming is what it does best - and Quake has plenty of that.
Its native 320x240 resolution also helps, though its 16-bit color display doesn’t. Support for 16-bit color modes will have to be implemented into Makaqu’s renderer, and since this handheld doesn’t support CD audio, uncompressed WAV audio streaming will also have to be implemented.
OGG streaming could also work, but since OGG decoding slows down the Dreamcast version by a few frames per second (which is a significant amount, given how slow it is), uncompressed audio is a safer bet.
The lack of an analog stick should hurt the gameplay. Makaqu’s horizontal autoaim should help a bit, and its “function shift” feature may help may help in some cases, though the Dingoo has enough input buttons for aiming (d-pad), moving (Y, B, X, A), jumping (L), attacking (R), cycling to the next weapon (Select), toggling the zoom (Start), and toggling the main menu (Power).
As for the speed, it should end up running at framerates similar to the framerates in the Dreamcast version.
There’s already a Quake port for the Dingoo, so you may get an idea of how it should perform by watching this video. Every optimization should help.