I actually came up with an idea like this a while back:
I had always envisioned a certain type of Legends videogame. The opening introduction of the game would be the regular season one opening, but after the pendant flash, instead of panning the temple, it would show clips from the game. Once the introduction was finished, it would transverse into the opening the screen which would feature Olmec from season 1 with the two torches in front of him, with a list of 4 choices: New Game, Load Game, Options, and Storeroom. (I'll conjecture more on the Storeroom latter)
A new game would start you in a season 1 episode, a Season 1 Introduction would follow, when we "meet the teams" we are shown their names and attributes (speed, stamina, etc) and then we select one of the 6 teams. As Nickledgends said, the Wii remote would not work well for the moat crossing, as such it would call for timing and what not, shouldn't be too hard with a controller. The Steps of Knowledge would work the same way, except this time, when you buzz in, a list would appear with the 3 choices. Depending on the intelligence level of your team (shown at the beginning) the choices will change deepening on how far into the question Olmec was, of course if we wanted to, we could still add in a few kids saying: "Bow and Arrow skills?" or "A musical thing that does a jig?".
The Temple games would be relatively the same. That's one section of the show that I could see transferring into the game fluently. The Temple run would also be the same, except the prizes would be announced in the form of money (it would not be relative to the cost of the prices in real life). Assuming you beat the temple run, you could go on to a few other Season 1 layout 1 games (Despite the fact that there were only apparently 2 in real life) or you could go to the Storeroom, use the money you won, and buy a few new things. 1. You could buy the rest of the layout 1 Legends, 2. You could buy new temple games or moat crossings, or 3. You could buy the next Season 1 layout (once you have all of them, Season 2 would be for sale, keep in mind that with each layout you buy, the next one will be more expensive then the last.)
When you finally beat all the Legends, you'll unlock a temple builder device that would let you edit the temple anyway you like, turn any room into anything, have the wheel room in the ledges, turn the vipers nest into the Sacred Markers, the room would transform perfectly into a form of the room that would correspond to the room you are trying to turn it into (I realize in extreme cases that would be impossible, but try and use your imagination here).
Anyway, that's how I'd like to do it.