The degree Einstein received in 1901 was actually a teaching certificate in physics, something that would qualify someone to teach as a university lecturer. Such things don't really exist these days (at least, not in the English-speaking world) since, as you say, a PhD is generally a prerequisite to be a university lecturer now. However, professors—those who both taught and did research—still held PhDs then, as they do now. Einstein's original ambition was just to be a lecturer. As a physics qualification, it appears his 1901 certificate was comparable to a modern bachelor's degree. That is, comparable in an abstract sense, the actual content would have been rather different—as much of what contemporary students study past their first year hadn't been discovered yet (in many cases by Einstein).
However, Einstein did later complete a PhD, though in a somewhat unconventional manner. He was unsuccessful at finding work as a university lecturer so he took a job at a patent office. In his spare time, he worked on physics and wrote a doctoral thesis without being affiliated with a university. He submitted it the University of Zurich for consideration and they awarded him a PhD in 1905. That was also Einstein's so-called "miracle year" of multiple ground-breaking publications (including special relativity) and within a few years he was offered a professorship.