EmulatorJS seems nearly identical, though it requires a bit of initial care and feeding via the backend admin page to find all the menu art.

an example docker compose file:

  version: "2.4"
  services:
    emulatorjs:
      #from the linuxserver.io fleet
      image: lscr.io/linuxserver/emulatorjs:latest
      container_name: emulatorjs
      mem_limit: 1g
      cpus: 3
      environment:
        - PUID=1000
        - PGID=1000
        - TZ=America/Chicago
      volumes:
        # must declare inner folders before the global data folder
        - "/path/to/folder/NES:/data/nes/roms:ro"
        - "/path/to/folder/SNES:/data/snes/roms:ro"
        - "/path/to/folder/Atari_2600:/data/atari2600/roms:ro"
  
        - ./data:/data
        - ./config:/config
  
      ports:
        #admin and config page
        - 3000:3000      
        #frontend
        - 80:80

you can try https://nes.party or https://snes.party offers online multiplayer as well :)

Is there a browser API that can list files in a directory?

No