Assuming baseline competence as far as the simulation and buttons then it is all in the screen for me, and most of these replications/revisits/recreations have been woefully poor (they usually just seem to crowbar either a phone screen they found in their electronics vendor or on rare occasion the cheapest and nastiest replacements they can find). I have never met a non multiple algorithm I care to see, much less one that would do and work in real time on a device like this, so we will go with multiples for the purposes of my contemplations here. Would be nice to see something but if all they want to give us is nearest neighbour then I am more than OK with that.
They say
1600x1440 at a fairly high DPI (can't be bothered to figure out the resulting size right now)
Systems mentioned in the OP
Game Boy, to Color,
http://bgb.bircd.org/pandocs.htm#gameboytechnicaldata
Resolution - 160x144
to Advanced. The addition of a d in advanced does not speak to much care but still GBA)
Display 240x160 pixels
http://problemkaputt.de/gbatek.htm#gbatechnicaldata
or even Game Gear
Resolution: 160 x 144 pixels
https://segaretro.org/Sega_Game_Gear#Technical_specifications
Atari Lynx,
- Resolution: 160 x 102
https://atariage.com/Lynx/history.html
and Neo Geo Pocket Color
RESOLUTION 160x152
http://www.captainwilliams.co.uk/gaming/ngpc/ngpc.php
Ignoring pixel aspect ratio for now
So for the GB/GBC that is a clean 10x multiplier for a complete fill. I dare not speak the supergameboy's name but if they did want to give me SGB mode bomberman then I might lose some objectivity/cynicism.
For the GBA that is a clean 9x multiplier vertically, 6.6666666666666 horizontally. In that case doing a 6x multiplier (rounding down) vertically that gives 960 pixels or 66.6666666...% screen fill vertically and not quite there horizontally. Not looking great.
For gamegear then same as GB/GBC then (a 10x scale). I should also note the gamegear can play master system games (
https://segaretro.org/Sega_Master_System/Technical_specifications says "Screen resolutions: 256x192 and 256x224. PAL/SECAM also supports 256x240. Overscan resolution: 342x262 (NTSC), 342x313 (PAL) Scanlines: 262 (NTSC), 313 (PAL)" but we will have to wait and see what goes here for that one, and frankly I don't know how it handled it normally -- I played a few on one back in the day and it was great* but this was before I understood much of anything here -- it would be maybe 2 years before I took up emulation in earnest, and longer before ROM hacking/programming enough to do much here).
*that cart acting as a sun visor action... mind blown.
Edit I am told the GG pixel aspect ratio changes the game a bit here and its ratio is a bit different as a result. Take what I said above with a pinch of salt in that case.
For the Lynx then for horizontal fill (160 pixels like the others mentioned for 10x multiplier) then better part of 71% vertical.
For NGPC then we can't do full 10x horizontal without vertical cropping. Going with 9x then 95% vertical fill, 90% horizontal.
So anyway clearly a GB/GBC and GG focus from the screen side of things, does not mean the rest will be an afterthought but does dampen my enthusiasm a bit.