The mirrorless camera has a lot of benefits for a filmmaker. Unlike a DSLR, which has a mirror in front of the sensor directing light to an optical viewfinder, a mirrorless camera gets rid of the mirror entirely, making for a smaller, lighter, simpler-to-manufacture camera without optical viewfinding. However, if you are shooting video on a DSLR, you aren't using the optical viewfinder anyway, so it's a natural evolution for filmmakers to embrace mirrorless cameras. Why carry around that extra weight and complication for a feature you never use?
This might well replace the T2i as my recommendation for an entry-level camera for the beginning or student DP.
This is a reason behind the popularity of the Sony A7 series with filmmakers: smaller bodies with the same images you would get from a DSLR. In addition, if you take advantage of a mirrorless lens mount like MicroFour Thirds, lens design can also be closer to the sensor.