If you open the .cue file in a text editor like Notepad, what do you see? Does it reference files that are missing? In that case you might want to try getting those missing files and putting them in the same directory or getting another pre-patched copy of the game. archive.org appears to have some. Or you could get a clean rip of the original Japanese disc and patch it yourself (
https://www.romhacking.net/translations/846/).
If it's the emulator that's the problem,
https://emulation.gametechwiki.com/index.php/PC_Engine_(TurboGrafx-16)_emulators recommends Mednafen, ares, or Mesen.
In the past I think I was able to get a .bin+.cue rip of the original Japanese disc working by using a Mednafen (beetle) libretro core. I didn't need to have it mounted as a disc on my PC like you appear to be trying to do. I think I was able to launch it by selecting the .cue file.