It is not us that are experiencing motion in space rather than time, it is the other observer, as far as we are concerned. We are in essence being egocentric and imposing our concept of time onto someone else, even though that other person has a clock and is perfectly capable of constructing their own concept of time based on that clock. If we forget about gravity and acceleration for the time being, so deal only with "inertial frames" of reference, then our own frame is always completely stationary, so is moving "entirely through time" at rate unity. But we can conceive of other observers in other frames who are in motion, so some of their movement, from our perspective, is through space, which means less of their movement is through our concept of time. That's why we interpret them as moving more slowly through time than we are, even though they see themselves as stationary, their own clock as working fine, and we who are moving partially through space.