The answer to this question really depends on what you mean by “support” and “video”:
If you “just” want to query/receive/transfer DICOM videos, Orthanc will work fine either with 2D+t or real videos (because Orthanc is a Vendor Neutral Archive). This distinction is also discussed in another FAQ entry.
If you also want to play the videos, to the best of our knowledge, there is currently no Orthanc plugin for H.264 or MPEG2 (though such a plugin should be developed in the future). However, if your video is a 2D+t (cine) sequence, Orthanc can already display it inside a Web browser by at least 2 different means:
To summarize, if your video is not encoded with MPEG2 or H264, OR if you do not need to play the video within a Web browser, Orthanc actually supports video.