If you look at some of the written instances of...
He had a sense of grandeur about him
...it should be reasonably clear that in most if not all of them, the primary point being made is that people around him had that perception (but feasibly the subject himself wasn't even consciously aware of this). On the other hand, if you look at written instances of...
He had a sense of grandeur about himself
...I think you'll agree that they mostly refer to the subject's own perception of himself, and/or the image he wishes to project.
TL;DR: The (far less common) option of using a reflexive pronoun in such contexts puts more focus on how the subject presents himself.
The normal non-reflexive pronoun works better for the more common nuance (how other people perceive him).
Consequently, it's perfectly possibly to say of something "non-sentient" (such as Darwin's Theory of Evolution) that there's a sense of grandeur about it. But you'll probably never encounter a sense of grandeur about itself.