Well media shifting in UK is tortuous (without a license from the copyright holder) -- it was briefly legal a couple of years ago, but the liberalisation was reversed -- so you'd have to be using the original media. Elite on BBC was on tape (LOAD "PROG" !), so you'd need to load from the tape. I'm not sure about the legality of emulators, as long as you don't copy without a license to make them then they should be OK; it's not something I've looked at the caselaw on though. Emulation might be ruled out by user licenses, but I think in the case of Elite, say, that they'd predate the notion of running games under emulation. Nintendo presumably wouldn't license newer copies and allow emulation.
I'd doubt that they loaded it from an original tape.
Nostalgia for old games and TV/Film is a massive thing at the moment (and probably always, going forward) but copyright law's extensive life+70 protection periods has a chilling effect on the lawful enjoyment of such nostalgia in my personal opinion.
I'd be interested in a source for that.