What makes an experience “mystical?"

You ask how a non-physical entity can have a shape. The religious and mystical literature is replete with visions of spiritual beings with size and shape. I would question the assumption that spiritual or mental things invariably lack physical properties such as extension. In modern times, this assumption is inherited from the Cartesian dualism of unextended mind and extended matter, and look how problematic that turned out to be. 

Extension no longer makes sense as purely a physical property. Especially considering that it makes more sense for physicality to be considered as just a subset of mental or spiritual phenomena, albeit shaped by the senses which are also provided by the physical avatar we incarnate into and perceive through.

Any phenomena that can become a field, of whatever nature, has extension, whether in physical space, astral space, mental space.

In a mystical experience... as you've noted in other threads, perhaps the experience is of the Cosmically Immense Soul ~ every Cosmically Immense Soul sharing the same core nature, despite every CIS being a distinct individual energetically.

So... a mystical experience would therefore imply that every single incarnate individual is a divine being in their true nature, a "god", if you will.

(Of course, you get some individuals who then ask why incarnate into pain and suffering if we're so perfect and powerful and infinite? Why do we need to learn or grow or anything?)