I was trying to search this up, as I had no idea if they played a RAW video, with no color compression, or something like 10-bit color-depth?
A Sony 4K Cinema Projector claims to use an LMT-300 server that supports the DCI DCP standard: http://us.digitalcinema.sony.com/pro/product/digital-cinema-digital-cinema-projectors/srx-r320p/features/#features
The DCI DCP Standard claims 10 or 12-bits per color channel (30 or 36-bit RGB or YCbCr): https://en.wikipedia.org/wiki/Digital_Cinema_Initiatives#Image_and_audio_capability_overview
As a side note, RAW video at 48 fps, 4K (4096×2160), with 36-bit pixel depth would equate to:
(48 * 4096 * 2160 * 36) / (1024 * 1024 * 1024) = 14.23 Gibps
... roughly 15 Gigabits (Gib) per second of video. A Bluray Disc XL is only capable of holding 128 Gigabytes (GiB) (8 bits per Byte), equating to a total of roughly 69 seconds of video -- no sound, no metadata, no subtitles, nothing but imagery.
RAW video is entirely unfeasible with current technology.
Yes, you could upscale a smaller sized RAW video, but even with 24 fps, 1024x768 (XGA), 8-bit RGB, you would have:
(24 * 1024 * 768 * 24) / (1024 * 1024) = 432 Mibps = 54 MiBps
For a 120 minute movie (120 * 60 = 7200 sec), you would have:
(54 * 7200) / 1024 = 379.69 GiB
... that's almost 3 full Bluray XL discs, just for the video, no sound, no metadata, no captions, no menus, nothing but video, 3 full XL BD.
IEC Notation reference, see table at top right of page: https://en.wikipedia.org/wiki/Megabyte
(JEDEC and Metric notations cause confusion, thus sometimes the encouragement for the IEC notation)
There are a variety of projection technologies in use today, so there's no single answer. However, for digital projection, no, they don't use RAW video. It is definitely compressed. This wikipedia article suggests that the video either 2k or 4k and is generally 12-bit per channel, and JPEG-2000 compressed.
While corner-cases do exist, the theatrical distribution standard color depth is 4:4:4 12-bit and the standard color space is DCI XYZ. This is independent of resolution (most films are shown at 2K resolution and 24 fps) but at 48 fps the color depth is dropped to 10-bit (4:2:2). Note that very few films are produced at the higher 48 fps.
When projecting in 3D, 4:2:2 10-bit is used due to the increased bandwidth requirement of separate 3D images. 3D projection outside of Imax uses 2k resolution and 24 fps per eye.
As far as compression, lossless JPEG-2000 compression is used.
For more, visit the DCI Specification.