Here is a link to the actual medical article published in the American Journal of Obstetrics and Gynecology: http://www.ajog.org/article/S0002-9378%2812%2900023-3/fulltext
The article cites that the type of MRI used is "preferable in pregnant women." and that a number of studies have shown no increase in fetal harm.
Mom showed up in labor, spent the first stage of labor birthing in bed, was given an epidural and then transferred to the open MRI where she pushed the baby out.
What was the goal of this you ask?
"Our main goal was to describe the relationship between fetal movements and position as the fetus passage through the birth canal, using an open MRI scanner."
After watching the video, using my (untrained) eyes, it does not seem to me to give much more information than an ultrasound could. As the article mentions, "Today the cardinal movements can be studied with sonography."
But it is pretty neat to see!