What they're doing is simply "Star Trek Season 4." There are lots of fan films out there that take place in different eras. All of these reflect the primary interest of those making them. Fan film: a film made by fans. Fans = Fanatics. Either watch it or don't, why all this twisting about "being able to go forward" or whatever? Star Trek was never supposed to be a real look into the future. In fact, it was about 1966 man in a future time, so it never would have been accurate. Every technological invention of the series was made to be recognizable to that audience. It was always closer to "present day" than to 2200-whatever.
Also, why does it have to be "relevant?" Why can't it just be a fun visit to a series that many fans think should have had a 4th or 5th season? I wonder, does Star Trek's brand of Message Television even need to exist? Think about it, the taboos of the past are gone. People drop swear words on network television. We have nudity, frank discussions about sex, politics, terrorism, school shootings, racism, sexism, homophobia, racial profiling, and what have you. The time when it was necessary to hide these subjects behind "Martians and zap guns" is way over. Actually, redressing it to make it palatable for the masses is seen as soft and cowardly now. That part of Star Trek's intention is pretty much obsolete. All it really should be required to do now is tell mature, smart sci-fi stories with good characters, in an entertaining way.
Everyone's taste is different, but the reason why Star Trek Continues is presented like this is because that's they era of Star Trek they love most and are most interested in. It's season 4 and it was a fine premiere.