Three-Finger Swipe Between Spaces (Desktops) No Longer an Option?

I just upgraded to OS X Yosemite 10.10.4 on my mid-2013 MacBook Air. Now I am unable to use the three-finger swipe gesture to move between desktops (or "Spaces" as Apple Support refers to them).

I went into System Preferences for the trackpad to try to fix it, and it doesn't even offer an option for switching between Spaces anymore at all. In place of the three-finger swipe for Spaces, there is a three- or four-finger swipe option to switch between full-screen apps, which is NOT the same as Spaces and is not of use to me. (I never use my apps in full screen.)

Did they really just eliminate any option for a gesture that switches between Spaces? It looks like I can download a third-party app that gives me more customizable options for the trackpad, but it seems insane that I have to experiment with third-party software just to get a gesture to switch between Spaces, which is supposed to be a major organizing function of OS X.

Am I missing something obvious?