Some are based around YCbCr (aka YUV) PQ HDR10 or HLG 10-bit HEVC/h.265 and then Dolby Vision RPU metadata (and in some cases also an expansion layer to get from 10-bit to 12-bit depth). These can usually be replayed with no Dolby Vision licensing requirement for the HDR10/HLG stuff. Examples of this type of DV sources are Dolby Vision UHD Blu-rays and DV video shot on iPhones.
Other DV stuff is encoded purely in a DolbyVision video format using ICtCp representation and PQ instead of YCbCr/YUV - though still encoded in 10-bit HEVC/h.265. When these are replayed by non-Dolby Vision licensed devices they replay with magenta/green colours instead of normal colours, because they are interpreted as YCbCr when they aren't. This format is widely used for streaming platforms - where the streaming player can request a specific encode that it can play (rather than a single encode needing to be playable by multiple devices). The CoreElec DV implementation can play these OK, few other devices can.
Is there an easy way (e.g. using mediainfo, what is the relevant string to look for) to see which case a video is in?
Do you believe the first case here can be decoded and displayed correctly, purely by outputting the untouched YCbCr data from decoder and the appropriate metadata? I believe the second case requires per-pixel processing which is likely infeasible at 4k without dedicated hardware or a very high performance gpu.