What gave me this idea is the fact that, when you first meet house, he says that he's "...flesh and bone, not silicon." Why would he mention silicon in a world where transistors didn't exist? There's more evidence however. One of the biggest advantages of transistors is that, they can be made very, very small. Sure, vacuum tubes could have gotten much smaller since the 1950s, in fact, some 60s transistors are about the size of a pencil eraser, and such "microtubes" are also personal headcanon. Nonetheless, the question is one of how small we can make tube-powered computers. Transistors could have led to a dramatic increase in the intelligence of robots and helped make RobCo the robotics giant it was.