There's more at stake here than just a movie though.
What I mean by that is: video games have a very long and generally poor track record of translating well into movies.
Look at what happened with Activision-Blizzard after the Warcraft movie flop. They completely pulled back on having outside studios work on their IPs.
The same happened with Nintendo after the '93 Mario movie which is still one of the weirdest movies ever made. Except for Pokemon anime, they've been very wary of letting outsiders work on their IP.
They're really going to want to have a lot of input and make sure that this movie is successful, and a part of that is 1) Nintendo having significant input such as Miyamoto as a producer who can have real input, and 2) making sure that the movie has a strong sales push behind it.
I'd imagine that Universal offered more on both accounts than others especially due to the fact that a strong vertical push for SNW can combine with selling the movie(s). Giving Universal an important stake in the IP through movies helps to tighten the overall relationship.
And let's be clear here, if this is successful, it'll go much farther than just 1 movie.
This is a movie that Illumination needs to hit out of the ballpark everywhere but especially in China.
If this movie does well worldwide, expect sequels and the possiblity of a Zelda movie.
If the movie does well in China, that opens the door for SNW to go to China as well.
The stakes are very high here to put it mildly.