This makes the most sense. I don't think it's necessarily a shared counter in the idea that it switches between different airlines during the day, but probably owned by the airport and the airlines leasing space don't have much freedom to change the setup. There counter looks generic and then the wall is covered in LCDs displaying "Alaska Airlines" and all of their upcoming flights. So it's possible it's just the ticket printer that MCO provides with the setup.

I might just need to take my gripe to MCO instead of Alaska, although I can't remember anyone else having this same ticket layout from MCO.