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.