As Journeyman Geek pointed out, a recompile is necessary first to target the ARM processor.
I've found some steps documented here as how to achieve this:
Compiling Desktop Apps for Windows RT
The method above produces an ARM executable, however when its run on a Windows RT device, it results in the following error message:
Windows cannot verify the digital signature for this file
There's some further detail here regarding possible ways to circumvent this error message:
And an ongoing discussion on StackOverflow here:
UPDATE (JAN-9-2013) - EXPLOIT BY CLROKR
A developer by the name of clrokr has come up with a method of getting arbitrary desktop applications to run on Windows RT without having to sign them.
The method used is by hacking a single byte in the Windows kernel...
... deep in the kernel, in a hashed and signed data section protected
by UEFI’s Secure Boot, lies a byte that represents the minimum signing
To do this requires the use of a remote debugger every time you want to run the application, so its not an easy hack to make use of, but in time will probably be improved upon to the point there is a simple jailbreak-type installer.
There's some more information about people using this method here: