Gifpress
From Just Solve the File Format Problem
Gifpress is a special-purpose file compression utility for DOS. It compresses only GIF image files, to its native .GPS format. It was developed by John Callicotte, and distributed as shareware.
A GPS file can be decompressed back to a GIF file that is functionally identical to the original, but not necessarily byte-for-byte identical.
Format details
There's clear evidence that Gifpress uses the Cx data compression toolkit (v2.01) by Eugene Nelson and Four Lakes Computing (cx201e.zip).
Identification
It's not known how to identify a GPS file from its contents, though in limited testing, the bytes 0xff 0xb4
always appeared at offset 2.