While the console market has been mostly dominated by the Big Four, which do you think is the best console that's not from Nintendo/Sony/MS/Sega, and what makes it worthy of the top spot in your opinion?

The Atari 2600. It's basically the grandfather of gaming.

Even if the Odyssey was the first console, it was thanks to the Atari 2600 that gaming become popular.

The Atari 2600 is the obvious answer, though it's really hard to judge from modern standards, even much more so than third gen hardware.

Otherwise, the PC Engine had a pretty solid lineup. 

I got a personal soft spot for the Neo Geo AES.

The perfect arcade experience at home. Blew my mind how massive the cartridges were and how great the arcade stick felt to use.

I like that you include Sega and even call them "the big 4" even though their last console is 27 years old. But to be fair Genesis and Dreamcast world be too obvious and boring answers, so I get why you would do that.
I wish I could add to the conversation, but I never even saw with my own eyes a console not made by those.  ̶D̶o̶e̶s̶ ̶t̶h̶e̶ ̶S̶t̶e̶a̶m̶ ̶D̶e̶c̶k̶ ̶c̶o̶u̶n̶t̶?̶
MSX had Metal Gear 1 and 2 I guess.

I think it has to be Atari 2600, it walked so that later consoles could run. It's successors, 5200 and 7800, were both sales disasters moving less than 2m each, but 2600 sold a very strong 30m units and had many popular games. 

PC Engine/TurboGrax-16.

It has a fantastic library of Platformers. RPGs like Ys and Cosmic Fantasy and Far East of Eden to having the largest shmup library of any console of the era. Literally over 100 Shmups. It had some good arcade ports. Created Bonk and stuff like Legendary Ax and the best version of Castlevania Rondo of Blood. 

Atari 2600. Wont elaborate.

Objectively, Atari 2600, for all the obvious reasons. There is pretty much no industry in "video game console industry" without 2600.

My personal go to is ColecoVision for its "arcade games at home" mantra and delivering on it in '82, launching with Donkey Kong, and for being direct influence on Famicom.

I never owned a console outside these four. Adding "home computers" would make this more fun, not that there are many home computer fans around here.

MSX and Amiga were cool. Sharp X68000 was godly graphics wise, but I've never seen one in person. MSX gets my vote since it's the reason why I'm a gamer. I was born too late (1987) to appreciate the Atari 2600.

I barely have any console experience outside Sega, Nintendo, Sony, and Microsoft. PC Engine is the one I'm most interested in trying out (Recently beat Rondo of Blood on PS5. Cool game).