On a technical level, if nothing else, I think that's a good achievement for a nonprofessional production.
What qualifies it is "non-professional" in your mind? Every member of the Axanar cast and crew on the shoot was a paid professional, with expertise and experience working in Hollywood. They were all paid for the shoot, no volunteers. Sounds pretty professional to me.
I can only speak for myself, but it's apparent to me that this is a nonprofessional production in several capacities.
From the presentation of the Vulcan scene (with things like those "camera shakes" discussed here in this thread) but more importantly simply by virtue of the fact that it's still a fan film. Hollywood professionals don't cobble together to make movies using other companies' intellectual property. This is a film made by fans first and foremost, and starring a fan who before this film was not a professional actor.
None of this is an indictment or a negative in my opinion, just a pragmatic look at your question. It'd be easy to also point a finger at the financing of the production as problematic, or at the very least concerning, but I don't know enough to comment on that.
If I were someone associated with the production however I wouldn't hung up on this "fan film vs. indie film vs. professional film" nonsense. It's a waste of time; until CBS comes out an announces it's making Axanar itself, Axanar is always going to be a fan film.
Instead, I'd take Dennis' comment as high praise - he's saying Axanar has achieved a look similar to what one of the professional series (in this case Enterprise) had done on a regular basis a decade ago. Not many fan films can make the same claim.