I discovered this by sheer luck. To reproduce:
a) have an admin on your box (let's say "hero")
b) have a regular user on your box (this one's "loser")
c) log on as hero and install the game [installer runs with admin token]
d) log off
e) log on as loser and start the game [regularly or with admin token]
What happens is basically zilch: there's no sign the game was started. I didn't bother tracing with process explorer/monitor or the like.
After uninstalling I ran through the same procedure as above, with the same result. For some weird reason I tried the following
a) make "loser" an admin
b) log on as loser and install the game
c) start the game
I repeated process 1 with "loser" already being an admin before even installing by "hero", with the same results (only runs when previously installed by admin-loser). This makes no sense at all, requires elevated privileges Redmont finally (albeit in a horribly bad way, as usual) tries to avoid, and is completely non-intuitive and impossible to find out, except by the abovementioned sheer luck.
Meh. I'd love to see this fixed ;-/
P.S.: Ah, I forgot to remind everybody how hilariously great this game is :)