Surely, one can think without language.
1 KOSSLYN
Nobody has mentioned Kosslyn (Images of Mind, and Wet Mind; rather than the the
former books).
He has precise neurological evidence that imagination is a form of perception.
2 ORIENTEERING
I'm doing orienteering: you are given a map, and have to find a dozen beacons
in the woods. It's often a mix of verbal and spatial skills, but often, I would
say, it's (almost?) purely spatial + stragetic ("if I cut through there it may
be shorter, but a harder climb" -- where you visualize the scene and "feel" its
difficulty without having to name things).
3 SPATIALITY IN A WINDOWED COMPUTER ENVIRONMENT
You go through overlapping windows, and swap applications, with more spatiality
than verbality.
4 PROGRAMMING
To schedule the editing of several passages affected by a change, you have to
bring in spatiality: add that function, add a global at the beginning of the
code, ensure that the function is called and its result read, possibly from
several points, etc.
Of course, apart from thinking ahead of all the spots to change, it is useful
to evoke the names of those functions and parameters.
JFD