They mention other cloud platforms as competition, and Azure has a CDN. I doubt Github would switch anytime in the near future, but the dangers posed to smaller companies by the consolidation under giants is interesting. What happens when your competitor doesn't just try to steal your clients, but can actually just acquire them?
They also mention one risk as their dependence on AWS, a competitor, and that if all the cloud providers blackballed them, they'd be in trouble.
I'm sure Azure would welcome competitors to use their product - same way AWS welcomes Netflix. A good analogy would be Amazon switching from Oracle to AWS based solutions. In which case, they do have something to worry about.
For the Github thing, you're right, it's a different situation.
Though they also have several media heavy companies besides Vimeo highlighted in their case studies. Including: Wistia, A&E, iHeartMedia, Shazam, 7Digital, and FuboTV