These are apparently the oldest commercially released video games having to do with surviving a zombie attack:

Entombed, for the Atari 2600:

http://www.mobygames.com/game/entombed

The game cover is rather misleading, though, as it shows an archaeologist being attacked by a ghost, not a zombie:

https://atariage.com/box_page.php?SoftwareLabelID=165

Zombies for the Sinclair ZX81:

http://www.mobygames.com/game/zombies-sword-of-peace

In this case the game cover fits the theme:

http://www.zx81stuff.org.uk/zx81/tap...ays/.Cover.jpg

This one can be played here with the online ZX81 emulator:

http://www.zx81stuff.org.uk/zx81/emu...Sword+of+Peace

You = X
Zombies = Z
Potholes = 0

Fool the low-IQ zombies into falling into the potholes to win the game.

Both of them released in 1982.

If someone knows of an earlier example of a commercially released zombie-themed video game, let it be known here.