It's interesting that there's a company making such a high-quality retro device. That thing looks slick (and solid), and making a custom chip to run all of those games without emulation certainly shows dedication to creating a high-quality option. The upscaling is probably way overkill for most of those games, though I say that on conjecture, being too young to have played any.
One thing that makes games great is when they are made to look great on the technology of the time.
To be a pedant I have to note that this is not a custom chip but a FPGA which is a programmable chip (or class of such things). The distinction becomes more important as mere mortals (or at least electrical engineers without a corporation backing them) can have their own custom chips with considerable transistor counts burned in silicon these days in fairly small batch numbers (I don't know if we are quite in the hundreds yet but a thousand or so would work). I am expecting to see more of that in the years to come, somewhat amusingly the easiest in to such a field is to take your FPGA design* and turn it directly into a chip. Will also mean both the replacement part and the quality of fakes/repros will shoot through the roof, and that is before we get into improvements, but enough of that for now.
*FPGA stands for field programmable gate array, and if all chips are is an arrangement of transistors (the gate of a transistor being an important concept within it) then yeah. Not the most efficient way to make a chip (either as an FGPA or straight converting) but if it takes all the right inputs and spits out all the right outputs in the right amount of time and uses an amount of power that people can live with then so many people will argue the toss.
Considering the only reason you can legally make hardware clones of the Sega Genesis or the Super Nintendo is because the rights expired?
Nintendo could sue them if they still have he rights for the GBA.
And considering is only a few years since Nintendo lost the patent of the Super Nintendo hardware, because it expired, they probably do.
And let's not talk about the patent for software since the GBA did have an operating system...
Is not even a case of if Nintendo can win or not, just the fact they have more money and lawyers that the company making the Analogue Pocket.
Three main classes of rights here
1) Trademarks. These are essentially infinite but are more concerned with the name and logos. Some companies tried to include their trademarked logo in the code and thus get around things that way but were smacked down, others will press the logo into plastic or try to include the logo in the function (there is a reason fashion houses have their logo as a clasp on their bags and it is not because it looks cool).
2) Copyright. Length is probably north of 100 years at this point (or if you prefer we just started getting works from the 1920s become copyright free --
https://web.law.duke.edu/cspd/publicdomainday/2019/ ). Hard to copyright an arrangement of off the shelf chips. The BIOS files might be copyrighted but there are ways around those, and also the GBA did not have an operating system of any real note -- the BIOS is as about as close as it comes there and you don't have to interact with it, it does not run all the time or really do anything like a hand off to run the games, and when you do speak to it then it functions basically as a built in programming library (
http://problemkaputt.de/gbatek.htm#biosfunctions ).
3) Patents. Length varies a bit depending upon field and follow on patents (you tend to be given a few years to file additional patents that might use another which don't then conflict with yourself, part of the reason we had some troubles figuring out when the NES dpad patent ended) but the term (aka length) of the patent is around 20 years for most places and what you might have heard. Also tends to be a novel and unique invention, which is not an arrangement of chips. Some places do patents for software as well (most notably for this discussion the US and Japan) but other places (basically everywhere else) consider the very notion of software patents as completely opposed to the idea of patents (software is maths and you can't patent maths) and thus an abomination.
Assuming they don't use the name gameboy or suggest they are endorsed by Nintendo (repeat for other companies on the list) then no worries there. For copyright then other than the BIOS you can't copyright an arrangement of chips (the ARM7TDMI of the GBA is... well an ARM chip you could probably get a million dropped off to your door in a few days if you wanted, the z80 is also popular for decades now...) or arrangement of memory and this is also one of the reasons we can have emulators (the courts have considered other things). You do occasionally hear of individual game trademarks expiring but I doubt any of the companies concerned here (or their successors) will allow the main console ones to lapse any time soon.
There are a few other types of protections that could apply at some level (called different things in different places but design rights and registered designs act as lesser versions of some of those) but nothing likely to bother it here as they are usually reserved for shapes and colour schemes.
Nintendo probably could do the we have enough money to tie you up in court thing (assuming Analogue care to be based somewhere that will listen -- there is a reason various flavours of China, Russia and Eastern Europe are often bases for a lot of these) but them having clear cut legal basis for this is a different matter entirely. Assuming there is not some quirk of the DMCA (which I doubt as there are a dozen devices that would otherwise qualify) then best I could see happen there is they have some kind of weird physical patent for an aspect of it -- one of the flash cart makers for the DS said something once about Nintendo having a patent on the plastic spacers between the cart pins for the DS which is why they did not have them on their DS flash cart, however I don't know if that is true (never looked) and thin plastic spacers are hard to make in plastic (or at least it is far easier to have a blank spot) so that could just as easily be the reason.
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