It's also the 30th birthday of the ZX Spectrum, as rambled about here.
Plenty of the classic Spectrum games have Who-friendly plots.
A rogue general kidnaps an ambassador and flies off into space, so you have to assemble a rescue squad of aliens and robots.
On a dying planet in a distant galaxy, the last of the guardians store all of their libraries, records, and knowledge on a single starship together with cryogenically preserved members of their race. A single robot, Alien 8 is tasked with keeping these people alive. The ship is launched towards a new solar system and Alien 8 performs his task for thousands of years during the journey. However, as the ship nears its destination, it is attacked and boarded.
And naturally there were also Who-relevant games, official and otherwise, as discussed here.