I tried my best to get it reproduced with the binary ES install, but whatever I do on my side I land correctly at "Teenage Mutant..." which is the first with "T" (in Arcade) and at "Tecmo Bowl" (first with "T" in "NES" and "All Games").

As it is non-deterministic on your side I am leaning towards the hardware and maybe in conjunction with "ThreadedLoading" value="true" but it is a vague guess.

If you have the patience, you may install the whole shebang Retropie on your Desktop or in a Linux VM or if you have a spare Pi4 at hand use that. If it also happens on a different RetroPie installation it indicates something with the filestructure/gamelist data, if not then the plot thickens that it might be hardware related.

You made a good work.

@mitu I purchased a a four player arcade cabinet set to the original Ninja Turtles four player set up. A joystick and two buttons for each player plus a credit button for each. Honestly I'm very new to this and I'm learning little by little

Here is a really good list of good mame clones.
This lists out the 2 player versions of the popular 4 player games, as well as some other good clones ... ie fast Ms Pacman!

http://www.hyperspin-fe.com/forums/topic/406-mame-clones-worth-playing-a-complete-hopefully-list/