My son's Bargain Gaming Laptop ...
1) an old T420 from fleabay with a decent i7, 16GB RAM, 128TB SSD for OS and 1TB Hybrid SSHD for Content (£300 + £100)
2) a Village Instruments eGPU box with a PCI-E interface (£100)
3) a decent PCI video card for the above (£200)
4) (optional) external monitor (£200)
Not only does he get a cheap, tough laptop with decent battery life, but when plugged into the other stuff, back at the dorm, he gets framerates that challenge your average gaming laptop. Feeding the video back into the laptop, rather than an external screen, it's eminently playable (60fps on fairly high graphics settings for many games), but on an external monitor, the frame-rate for any given graphics setting is approximately double (I presume the constraint is the speed of the PCI-E).
Not as portable as any of these covetable boxes, but pretty good going for an impoverished uni student who is away from his home gaming rig for whole WEEKS at a time :-)