There's one game that is possibly my overall favorite, but isn't possible to play on the Dingoo. It is Star Trek: Tactical Assault
for the DS. Not the campaign / story mode, but the skirmish mode. Just random encounter after random encounter, it's a little bit more involved then just a plain shoot-em-up in that you do have some tactical thinking in terms of how you attack, what weapon to use, when, that sort of thing. The combat is 'real time' and you do fly around and shoot things, but with rather more thinking than, say, space invaders.
Another game I liked (going back a million years) was Red Storm Rising on the pc. Same sort of thing, not the campaign mode but the random encounter mode. You'd have to identify the target(s) then determine the best way to attack and choose weapons and defences and so forth, commanding the sub in 'real time'.
My thing is I generally suck at games, so I get bored with "campaign / story modes" very fast due to all the dying I tend to do. The skirmish / random encounter stuff is perfect for a 5 or 10 minute diversion, and I don't need to sit through some long introduction / backstory that lasts longer than I survive in the game!
I like the tactical stuff a bit more than the simple shoot-em-ups because there's some more thought involved, rather than just mashing the button at hoards of identical sprites.
If anyone could suggest similar style games to ST:TA or RSR that I could play on the Dingoo, I'd be very grateful!