Hi John, you mentioned previously that you had a Timex Sinclair 1000 so I would assume you knew how to use it. I had one in 1981 and remember it well. In MAME when you start it with 'mame64 zx81 astroids' you are effectively switching on a ZX81 with the asteroids tape in the attached cassette player. You need to tell the ZX81 to load the game from the cassette.
Here's a step-by-step to load the game:
Press J (should see LOAD) then SHIFT P twice (should see LOAD "") then press ENTER
You have now told the ZX81 to load something from cassette. If you remember back over 35 years you'll know you now have to press PLAY on the tape recorder. In MAME press SCROLL LOCK to Enable UI then press TAB to enter the UI menu. Now select Tape Control, then Play. You should now see the cassette playing. Press TAB again to exit the menu and press INSERT to FastForward the emulation to load the cassette quickly, the game will start when loaded.
I recommend getting the ZX81 artwork from http://www.progettosnaps.net/artworks/a ... p?letter=z
and placing it in your artwork folder so that you can see the keyboard layout like: