I finally figured out how to get the XBox controlled by the Broadlink RM Mini and ultimately with Alexa.
This video from Paul Hibbert was a huge help: [Link: youtu.be]
Basically, I used someone else's cloud remote to learn the code in RM Bridge. In the Broadlink e-Control app, search for Xbox then select the 'Microsoft' one (the video explains this around 6min). If you just want to control the xbox via Broadlink with the app, you can stop there. If you want to activate it with voice through IFTTT, though, then you need to learn the code in RM Bridge by sending it to the RM Mini while the RM bridge is in learning mode. I couldn't find this anywhere else online so I hope it helps.