In residential wood construction today, shear walls are almost always constructed of plywood panels specially nailed to the framing. They are common on exterior walls since there is often plywood sheathing anyways, although they can be interior. The diagonal piece shown in the photo may be a remnant of construction
Unlike vertical load-bearing walls, shear walls do not necessarily have to be continuous from the top of the structure to the foundation, although they typically are. So if there is no wall or foundation underneath this one that is a good sign.
However I should point out that building codes, especially seismic codes, have changed dramatically since your house was built. It may be impossible to tell if there was any seismic design done at all, unless the house has been substantially renovated. From some quick searching online it looks like seismic codes in California were not systematically applied until the 1960s. In the absence of dedicated shear walls, regular framing, drywall, etc. does provide a small amount of lateral resistance. I doubt that little wall was doing very much but technically you probably did weaken the structure a bit.