Look up the definition of “to spoon.” The Internet, quickly enough, will tell you that “spoon” is an old-timey verb meaning “to be amorous, affectionate.”There was another unusual word-- "Spoony", which was used in the 2nd advertisement. Webster's doesn't have a definition that connects with men's clothing fashion. It may have been youthful vernacular during that time period. (Input from others would be appreciated on defining "Spoony".)
In the early 1900s, “spoony” was an adjective that popped up now and then. You might not find it on the Internet so easily, but I did some research. I ran across the word in old newspapers. The context in which it was used leaves no doubt that it meant, logically enough, the state of being amorous, flirtatious, affectionate.
Thus, a fellow in the military who looked “spoony” while on leave appeared to be a fellow who was ready to give and receive some sweet romance. Or at least the semblance of it.