Yes, that study even found a g-factor.

This reasoning seems as silly to me as concluding that there can't be such a thing as general strength because bench presses and squats uses different muscle groups.

There is a paper by Pierce/Miller/Arden/Gottfriedson that explains some ways that genes can cause even seemingly unrelated biological phenomena to be correlated. These kinds of explanations should hold for more closely related biological phenomena (math/verbal/spatial skills) too: Why is intelligence correlated with semen quality?