No, by CPU is an odd choice, I meant for the i7-6700K. The Ryzen CPU is quite recent and very powerful, and energy efficient. Again, for a multimedia system you need a big case like the Define one and lots of SATA ports and bays. The Intel one checks the boxes, but you need a better processor or alternatively an external GPU, like the Intel Battlemage to have hardware encoding acceleration.
The mini PC is nice but not suitable for multimedia machine, as it lacks the SATA ports and bays. You can use it as a router, like OPNSense.
I mean you can exchange the network card with at least 2.5Gbps of your Intel computer, install Linux and create a share and use the Ryzen mini PC for managing and transcoding media files, but it will complicate your setup and won’t be very energy efficient.