First off, forgive my possibly unrealistic budget, incorrect terminology, lack of knowledge, and general woeful ignorance about PCs 
DS will be 16 this summer and currently has a very old PC that came from a relative, which constantly overheats and doesn't run many of the games he wants. He is such a good kid and although I know it really frustrates him he doesn't complain about it, he is just saving up to buy himself a better one. I have a budget of £500 for his birthday (much more than usual for various reasons) and would love to be able to get him one as a surprise.
He mainly plays historical, fantasy, or strategy games through Steam. He is not into racing, shooting, or sports type games, if that makes a difference to what is suitable.
He sent me these spec when I asked him what he was looking for: MINIMUM:
Requires a 64-bit processor and operating system
OS: Windows® 10 Home 64 bit
PROCESSOR: Intel Core i5-750 | AMD FX 4300
MEMORY: 8 GB RAM
GRAPHICS: NVIDIA GeForce GTX 660 | AMD Radeon HD 7870 | Intel Arc A310 | Intel Iris Plus G7 | AMD Radeon Vega 11
STORAGE: 20 GB available space
We did go to the local independent computer shop a few weeks ago to ask them but they were very very discouraging, saying we wouldn't get anything worth having for less than £1k and that even that was a low budget. They were meant to be getting in touch about upgrading some parts of his existing computer but they seemed to think even that would be very expensive and they haven't got back to us anyway.
Is it really not going to be possible to get anything for £500? Am I terribly out of touch with what things cost? I just know so little that I don't even know where to start!