For anyone with an older operating system, you might get an error about the right version of the .NET framework not being installed. Alternatively, when launching the game you might just get an error which (if you click through to see the details of the error) says it's a "System.MissingMethodException" error.

I fixed this by installing the right version of .NET. It's a bit tricky because you need a version both new enough to run the game, but old enough to be able to install it on Windows 7. You also need to dig around for the offline installer, because Microsoft's online (default) installer will just fail to download the software.

I found this was the sweetspot:

https://www.microsoft.com/en-us/download/details.aspx?id=40779

That's the offline installer for .NET version 4.5.1. Install that, reboot and the game should work.