OP's hypothesis is that people with an inner monologue can ONLY think using the monologue. It's easy to test that hypothesis.

step 1: create a text description of the pic-rel shape (i.e. translate the shape into the format that OP claims inner monologue people work with - words)

step 2: show only the words, not the picture, to a test subject

step 3: ask the test subject to rotate the shape about any axis, and then describe it

I predict that literally nobody is able to perform this task. That implies, according to OP's hypothesis, that people with an inner monologue cannot rotate abstract shapes in their head.

...but they can. So therefore OP's hypothesis is rejected.