All 4K video is not the same. You have not specified what codec your 4K video is, what bit rate, where you got it, etc. It is not possible to answer your question definitively without knowing this. However I'll speculate maybe it's H265.
I edit and play H264 4K video on my 2015 top-spec iMac 27 every day, and it will even play on my 2013 MacBook Air.
If by some chance you are talking about H265 4K, that is an entirely different matter. H265 is immensely more compute-intensive than H264. Even my top-spec iMac 27 cannot always play H265 4K without lag. This has little to do with the GPU per se, as H264 and H265 cannot be meaningfully accelerated by a GPU itself. The core algorithm is inherently sequential and not amenable to GPU-style parallelism.
H264 and H265 encode/decode can only be accelerated with algorithm-specific hardware logic, such as Intel's Quick Sync, nVidia's NVENC or AMD's VCE. This logic is entirely separate from the GPU although in some cases it is packaged on the GPU card but accessed with a separate API. None of these are automatically used, but the application software must make specific API calls to use it.
Ironically there are mobile devices with H265 hardware support integrated in a SoC (System On Chip) because the mobile market has rapid turnover and the large volume supports huge development budgets. The iPhone 6 and later use H265 for Facetime but not recording.
To my knowledge the only camera that used H265 was the Samsung NX1 which is now discontinued. Behind the scenes there has been a huge conflict over intellectual property and licensing fees for H265/HEVC which has slowed the rollout, also Google offers their similar VP9 codec for free. These delays have allowed subsequent codec development to bring into question whether H265 is even worth it:
http://www.streamingmedia.com/Artic...es/The-State-of-Video-Codecs-2016-110117.aspx