Tinker Board - is it supported by OSMC?

It is not supported by OSMC and I wouldn’t be surprised if it never is.

The SoC is Rockchip which does not have great support in Kodi. I believe only SPMC attempts to support this SoC and via Android. This is because they have implemented AV acceleration in a hacky way: i.e. not using the official Android method (MediaCodec) API. Team Kodi aren’t keen on adding workarounds as it adds a support burden in terms of maintenance.

The 4K support is not of much relevance because the board appears to only support H264, and almost all 4K content will be encoded in HEVC in the future.

Maybe the device will be supported, but it is not on the development roadmap. At this time, Raspberry Pi is effectively providing the same level of playback abilities at a better price and with better vendor support.