Yes, that trailer is turning up in more and more places. Unfortunately, it appears to be the only one so far, and it's just a short teaser. The movie comes out in May, so I expect there will be more trailers, but I am impatient to discover if the script has any chance of being as good as the cast and production values appear.
It looks like they'll be blending real life events with the stories they inspired Tolkien to write. (There is a glimpse of Edith dancing for him in the woods, which we know she did, and that it was part of the inspiration for the story of Beren and Luthien.) That could work, but could equally be fragmented and confusing (especially for viewers who are unfamiliar with The Silmarillion as well as LOTR).
Looking forward to learning more, since if the reviews are good I expect I will be at the theater on the first day with my ticket in hand. On the other hand, I don't want to get my hopes too high only to have them disappointed.