It is not the game that is the issue. It is the amount of data a video card has to generate for the 4K display. Think about that. Let's do some simple math for each of the recent generations of monitors.
HD: 1920x1080
Pixels Per Frame: 2,073,600
Data Per Frame: 7.91MB
Time to display full frame, at 60 FPS: 0.1667 seconds
Data generated per second: 474.61MB
UHD: 2560x1440
Pixels Per Frame: 3,686,400
Data Per Frame: 14.06MB
Time to display full frame, at 60 FPS: 0.1667 seconds
Data generated per second: 843.75MB
4K: 3840x2160
Pixels Per Frame: 8,294,400
Data Per Frame: 31.64MB
Time to display full frame, at 60 FPS: 0.1667 seconds
Data generated per second: 1,898,44MB
Nearly 2GB/second of data just for the frame buffer, has to be generated per second. It takes an incredibly fast piece of hardware to do that consistently.
From the HD monitor, you quadrupled the amount of data for each frame. That is a substantial leap.