I'd disagree, an 860m or 870m should be able to get solid FPS gaming on 1080p, which is around the 1K zone.
870m 1080p fps benchmarks
Link:
The Crew Ultra- 36.3, Dragon Age Inquisition Ultra- 25.3, Far Cry 4 Ultra- 32.9, Assassin's Creed Unity High- 26.2, CoD: Advanced Warfare Ultra- 33.8, Ryse: Son of Rome Ultra- 30.1
860m 1080p fps benchmarks
Link:
The Crew Ultra- 26, Dragon Age Inquisition High- 27, Far Cry 4 High- 29, CoD: Advanced Warfare High- 39, Ryse: Son of Rome High- 23
It's just a matter of whether or not he wants to game on his laptop. If he mostly expects to game on his desktop, my suggestion would just be to drop the laptop budget by like $300-$500 and get something far cheaper.