Consoles are personal computers crippled into (malicious) appliances.
Pretty much every single game console (except some of the budget "TV games") has been an universal microcomputer in the last ~30 years. Same hardware architecture and what not.
A computer simply takes a stream of binary data and executes universal instructions on it. It's like a sheet of paper: you can write/draw/paint on it (anything you like), fold it into origami (any you like), use it to build other things, wipe your ass with it…
However, console vendors have managed to (mostly) lock down software to control the user. When they couldn't do it technically through DRM, which typically doesn't work properly—then through legal bullying (think Linux on PS3).
Such an issue is even more serious, when a lot of the computing happens over networks and some of the appliances don't work properly without checking against vendors' remote servers.
Unfortunately, these behaviors are spreading to non-appliance computers too, "Universal Windows Platform" being a classic offender, and let's not pretend that Steam doesn't give Valve power over users' systems, major misuse only hasn't been publicized yet. Any supported Windows installation also has an universal backdoor anyway (as Microsoft can push any code they like as an "update").