The 1992 Game of the Year is Sonic the Hedgehog 2.
The runner up is Wolfenstein 3D.
The master thread for all of these contests can be found here.

Well it turns out the "Other" category got enough votes that there is a runoff including games voted on in the comments.  The results of this runoff will be decided Thursday, Oct 5 at 11:59 PM EST.  (There is basically only 24 hours to decide the winner.)

We are keeping 3 games from the original vote and adding 7 others.  First the 3 games that are being kept.

Mortal Kombat (Arcade)
Hot on the heels of Street Fighter 2 came this gory fighting game from Midway.  Mortal Kombat was also wildly successful, and it eventually lead to the creation of the ESRB in the US.  Mortal Kombat sold over 24,000 cabinets.  The home version of Mortal Kombat sold over 6.5 million units with the majority of those units being on the Genesis/Mega Drive.

Sonic the Hedgehog 2 (Genesis)
Sega released a second Sonic game causing Genesis sales to catch (and eventually surpass) SNES sales in North America.  Sonic 2 introduced Tails for potential 2-player gameplay, and went on to sell over 7.5 million copies making it the second best selling game on the Genesis after the first Sonic.

Super Mario Kart (SNES)
This first entry in the Mario Kart series would go on to sell over 8.7 million copies making it the 4^th best selling title on the SNES.  The series itself would sell over 175 million copies, a number that continues to grow rapidly to this day.

Now here are the 7 new games suggested in the comments:

Wolfenstein 3D (PC)
The FPS genre got its start with Wolfenstein 3D.  This is inspired by the 2 Wolfenstein games of the early 80’s even though those games had completely different developers and publishers.

RC Pro-Am II (NES)
Rare was making great games even back in the NES days.  In this case it’s the second game in the series about racing remote control trucks and cars.

Alone in the Dark (PC)
The first true 3D Survival Horror game.

Contra III: The Alien Wars (SNES)
Contra comes to the 16-bit generation on the SNES with Contra 3.

Super Mario Land 2: 6 Golden Coins (Gameboy)
This second Mario game on the Gameboy went on to sell over 11.1 million copies.

Streets of Rage 2 (Genesis)
This second entry is considered to be the best entry in the Streets of Rage series.

Looney Tunes (Gameboy)
A platforming game about the Warner Bros’ Looney Tunes characters.

Here are the games from the first run that didn't make the cutoff:

Virtua Racing (Arcade)
Star Control II: The Ur-Quan Masters (PC)
Ultima Underworld: The Stygian Abyss (PC)
Kirby’s Dream Land (Gameboy)
Shining Force (Genesis)
Dragon Quest 5 (SNES)

The year 1992 had a ton of notable games.  Here are some more games from this year:

X-Men (Arcade)
Ceasar (PC)
Alone in the Dark (PC)
Dune 2 (PC)
Indiana Jones and the Fate of Atlantis (PC)
Sensible Soccer (PC)
Ultima 7 (PC)
Wolfenstein 3D (PC)
Little Samson (NES)
Mega Man 5 (NES)
Super Mario Land 2 (Gameboy)
TMNT: Back From the Sewers (Genesis/Mega Drive)
Streets of Rage 2 (Genesis/Mega Drive)
Contra 3: The Alien Wars (SNES)
Final Fantasy 5 (SNES)
The Magical Quest starring Mickey Mouse (SNES)
Mario Paint (SNES)
Romancing Saga (SNES)
Super Star Wars (SNES)

This one is close, but I ultimately have to go with Mario Kart.
It's colourful, playful brand of racing created not only a megaton franchise, but a whole subgenre.
In classic Nintendo fashion, took an established genre and put a unique and incredibly fun spin on it, and the formula it pioneered lives on in spectacular fashion to this day.

I really want to give it to virtua racing just because of the fact that I was so impressed with its visuals back then. I could not wait for more 3D games. But just never got into it. All my quarters went to Mortal Kombat!

It had photo realism with simple yet smooth controls. You kinda felt like a ninja badass when you swept the legs. All the characters played the same so it was easy to play the field. The special moves were easy, but the fatalities took enough skill that you knew you were cool when you pulled one off 😎

Shining Force is amazing but Super Mario Kart is so nostalgic and gave birth to the most successful racing series ever.

Every one of these, I feel like the next years poll I'm going to vote for a non Nintendo first party game and than a game like Mario Kart shows up and I can't vote against it. Maybe 1993 will be different.

Wolfenstein 3d should have been an option in this one. I'm sure Doom will be in the 1993 list, but W3d was first...

I don''t think 1992 was the best year on terms of games. Mario Kart and Mortal Kombat are basically the most interesting games on the list.

My vote is going, shining force, will get decimated by Kart. I suspect Nintendo is going to win most of these polls till we get to 1997.

I have not played many of the options from this years poll. Pretty much only played Mario Kart, but I do not want to vote for that game since I do not think it holds up today. It did create one of the most widely enjoyed game franchises out there but I think every new Mario Kart game since is better and most a lot so. I have no desire to return to the original and the few recent times I played it, not even the nostalgia can make me enjoy it.

I have never played Dune 2, but since it is vital for the modern RTS genre I owe it a lot of respect.

One game released this year that I really enjoyed and liked on a recent playthrough is Super Mario Land 2 the six golden coins. Even if I liked it the controls have not aged well compared to other Mario games. It still have its charm and except for remakes it is in my opinion the best Mario game released on a dedicated handheld. Still not my pick for game of the year however.

My personal favorite from the year is a racing game, but not Mario Kart. Instead I vote for the late NES release by Rare RC Pro Am II. It did nothing really new. It did not look great. It had funky controls and releasing on the NES in late 1992 it was very outdated. But I just love that game. It is so much fun to me.
Many games had a bigger impact and I can't deny that they on paper and by most metrics are objectively better games. But since I do not have a clear winner for this year a personal favorite get the vote.