The article's conclusion isn't entirely correct. Mass on the wheels also affects braking (the reverse of acceleration), and handling (gyroscopes with less mass turn more easily). But otherwise, yeah, the standard line amongst racers is to upgrade your wheels before anything else (albeit racers do a lot more accelerating and braking that your average Sunday rider). Lighter wheels are like the SSDs of cycling: biggest bang-for-the-buck.

As a sidenote, the picture looks to be a late-1880s Columbia of some sort. Yup, same Columbia from whom you can buy a bicycle today (well, at least something bicycle-shaped; they haven't made good bicycles in over 100 years).