Regardless of what is posted here you absolutely need to have a PE (Professional Engineer) look at it in person and tell you what is going on. (There is NO WAY to only look at the photos and a floor plan and tell what is the actual makeup and function of the columns.)
But I'll chime in for something to do.
Let's just say that is a very interesting floor plan design. It seems this is a one story home. I am assuming a truss roof system? Pictures of the attic might explain things.
You mention your AC is above. If those 2 columns are needed for that, I would be shocked-typically the types of systems that require structural supports are chilled water systems with cooling towers usually at large buildings.
You also mentioned a 10 x 10 structure above. Is there a loft or storage room up there? That could be possible if the truss pitches are steep enough. The dining room is at the center of the home so that could allow for the maximum area above. So the columns might be there to transfer the floor loads from the loft area. (Again guessing)
If those columns are structural, and there is no loft above, then it is possible they are supporting a girder that in turn supports the trusses. Which even then is odd; the spans based on the floor plan are not that excessive and the columns are very close together with respect to the exterior perimeter. Further, why the columns could not be hidden in the walls is a mystery. The room is not that large.
Now it is also possible that *only one* of the columns is structural and the other is placed because they thought it would look really ridiculous to have a single unbalanced column in the middle of the floor, so the architect decided to balance it with a second column. (Not that having 2 columns in the middle of a 12 x 13 dining room makes any sense either.)
Lastly the actual column size is probably much smaller than what we are seeing; it is maybe a 4x4 steel column. (Given the high ceilings, I would be surprised if it the columns are wood, even if the home is wood framed). Then back to the idea of aesthetics-nobody wants to see a 4x4 steel column in the middle of the room, so they frame it out to make it look substantial and match the surroundings.
To beat a dead horse, I am just guessing since I really cannot figure out why the floor plan is designed like that. (Everybody in the thread is guessing)
Anyway, I'll close with what I said above-you absolutely need to have a PE look at this in person and tell you what is going on.
Thanks for providing an interesting diversion to talk about
Good luck !