I am the actual person that scored second place in the Final Fantasy 3 fewest steps to Mog contest. From my recollection, most of the Nintendo Power contests were games I didn't own/wasn't interested in, so I rarely entered these things, but I will share with what I remember.
The very first contest I entered was highest score in Super Mario Bros 3. This was somewhere in the late 80s or early 90s. I remember setting up Mario in one of those "infinity loops" where he would continually stomp the same koopa shell automatically as it ricocheted off the wall infinitely. I left the Nintendo console on for what must have been a day or two, and I amassed a score of maybe 3,000,000. I felt this was sufficient and took my picture and sent it in. I was shocked to find my score wasn't even close, as other players reached 99,999,999. I figured everyone must have cheated as the few days I left my console on gave me a paltry 3,000,000.
Fast forward a few years to the Final Fantasy 3 contest. I figured the game was kind of nerdy so not as many people would be entering it, so it was right up my alley and i was a shoe-in for first. I got all the way up to Mog, took my picture, and sent it in, and I was shocked to find I was "only" second. I thought for certain I would be first. But getting my name in the magazine was enough of an accomplishment for me.
I entered one other contest. It was a design Mega Man 6's robot masters. Being an avid Mega Man gamer, I already had drafts of a dozen or so bosses I dreamed up, complete with their special abilities, plus the powers Mega Man inherits, including their stages fully mapped out, mini bosses, Wiley's castle, and bosses. I sent all of this to Nintendo Power and nothing was used. I just remember the ones they published were far inferior to mine. The ones they actually used in the game were abysmal as well. If my memory serves me correct, Centaur Man and Knight Man were designed by Nintendo Power readers, though I could be wrong.
Some of my robot masters were Hard Hat Man(Originally Goomba Man but I was scared of being sued by Nintendo. I was a dumb kid, what did I know?), Axe Man(Originally X-Man, again, changed because I was scared Marvel would come knocking on my door.), and Blister Man, who was one of my personal favorites. I don't remember the others, but to this day I still believe my designs were better than the crap Nintendo Power chose to publish.
I also drew my own complete Donkey Kong Country 3 (Before they ever created the game), which I never submitted for any contest, and I think what I drafted up was better than the actual product they released a year or two later.
I also drew a dozen or so fighting games inspired by the arcade fighting game craze (Mortal Kombat, Street Fighter, Killer Instinct, Time Killers, Primal Rage, etc) Again, not submitted for any contest, just my own personal doodles and dreams of being a video game designer.
I may still have some of these doodles floating around if you're interested.