Of course. But the Shield is more capable than many devices at doing media conversion itself.
Others have reported that it will play 4K media and downscale to 1080p. HDR → SDR tonemapping is a feature in the Shield 8.2 software.
Here’s a screenshot of a Shield Direct Playing a 4K stream on a 1080p TV:
Perhaps the media is larger than 3840x2160.
Is it 4096 wide, by any chance?
But that’s all conjecture. Logs could confirm the reason for transcoding.