This 60 seconds is from a fake preview just before the end titles, and admittedly the most exciting part of the ten minutes. It has nothing to do with the main story. I put it up about 6 years ago. It gives an idea of how the whole thing was assembled. You might even recognize it from years ago. I did post it as an embed in a non-related TOS thread a few weeks ago, so I hope this isn't spamming. This clip's title is not the name of the full film.
Another user at YT had found the full thing and posted it, thankfully including the credits. It did get flagged for mature content (in the main story, Kirk gets it on with the guest star right on the bridge) and was age restricted, but there are no naughty bits on display though there is implied nudity and other suggestive situations. The main story is entirely on the bridge, so it's a bit static. Eventually it disappeared, so I don't know if it was due to the restriction, a C&D, or if the user just took it down himself, or the account closed.
I've been considering tackling it again in higher resolution since I have most of the project files, but my animation skills have not improved.