On a listserv of which I’m a member, Jerome McDonough points out that Tennis for Two is an analog game, so not only does it not require a computer, the medium itself — an oscilloscope — is an analog, so the information being represented on the screen isn’t digital at all.  An even earlier game, and the first game to use digital graphics, is Noughts and Crosses (1952).

This
page lists the source code for the world[‘]s first computer game and
incidentally the world[‘]s first computer based version of noughts and
crosses (tic tac toe).

This
is the original source code written by A.S. Douglas that was loaded
from a punched paper tape and run on the EDSAC machine. It is written
in an assembler. even for those of us who are unfamiliar with the EDSAC
instruction set and it’s assembly language some parts of the code look
reasonably comprehensible. The most impressive feature is it’s length –
this very short piece of code manages a good game of noughts and
crosses.

Keen to find out more? Then download the EDSAC simulator and the documentation from www.dcs.warwick.ac.uk/~edsac/ You can then follow this algorithm or try your hand at programming the worlds first programmable computer.