Decent Intel NUCs are ok price-wise, but definitely not cheap. A decent Linux-preinstalled box for my kid's Minecraft needs was about 800£ (non-basic Entroware Aura) here in UK.
It's a good machine technically speaking: perfect for lightweight gaming, office stuff, browsing, etc. But I suspect that a comparable mini PC from asian vendors would be twice as cheap and just as good. A laptop would be even easier.
I have tried a couple of pretenders and they were not up to the 24/7 load I have lined up, random reboots and lockups, maybe it was bad luck, maybe it was thermal management, either way the NUC keeps trucking.
There are Intel NUC laptops, or as they call them kits, I'm not sure what the details are. They're sold and branded by third parties but the guts are the same, except maybe the RAM and SSD (very minor customisation anyway). When I was looking I ended up with one since it was a pretty good price compared to the competition, I wanted one with a serviceable GPU for occasional games.
It's a good machine technically speaking: perfect for lightweight gaming, office stuff, browsing, etc. But I suspect that a comparable mini PC from asian vendors would be twice as cheap and just as good. A laptop would be even easier.