Many thanks to you all for your replies!
Further bushwacking through the Google jungle reveals that what may be happening here is a phenomenon called “Newton’s Rings,” in which a thin air space exists between a piece of curved glass and a piece of flat glass, and light reflects in a particular way between them, causing blob-like visual patterns resembling oil spills The only kink in this theory is that both the screen of the MotoX4 and the Supershieldz tempered glass screen protector are, technically, flat. Seems like the problem occurs more frequently with phones that have curved glass screens, onto which people try to apply flat screen protectors.
There are DIYers on YouTube who say they remedy this by removing the glass screen protector,
cleaning off all the adhesive around the edges, replacing it with a very thin piece of double-sided Scotch tape, and re-installing the screen protector using the tape. They claim that the Scotch tape is slightly thicker than the original factory adhesive, and that tiny additional thickness creates slightly more distance between the screen protector and the screen, and that increased distance is enough to eliminate the “Newton’s Rings” effect. I haven’t tried that method.
The company who makes the protective case I bought, Spigen, makes highly regarded tempered glass screen protectors for many Apple and Samsung phones, but not for the Motorola Moto X4. Instead, they recommend and sell a “nano liquid” screen protector that you pour onto the screen and let harden.
Does anyone here have any experience with this “liquid” type of product?