The Game Boy Advanced game Around the World in 80 Days (based on the recent Jackie Chan movie) features an appearance by Lord Kelvin:

Unfortunately, the game makers knew that Kelvin would kick Chan's ass if given the chance -- which they couldn't allow in this Chan-vehicle -- so Kelvin has been relegated to the expositively non-action-packed beginning and end sequences. Here are screenshots from the end sequence where Kelvin is attacked with vicious lies and falsely arrested (the programmers had to make him immobile to keep him from single-handedly taking out this gang of cretins):

Needless to say, this isn't exactly the best game ever made. However, as far as I know, it has the first appearance of Lord Kelvin in a video game. If anyone knows of any others, email me.