Cool little game, definitely would have seen that on a NES! You nailed the time period.
Now couple of fairly minor things:
The platforming could use a bit of user friendliness, check out coyote time and jump buffering, they both play a massive role to go from a dude that jump to a feel good platformer.
The other thing would be the respawn, going back all the way to the flag but not respawning the enemies makes it a drag; you could respawn in the room you die and it wouldn't change anything but save the player some time.
Overall a great entry you can be proud of that game!