I doubt this is a modern cipher. All modern encryption schemes typically output a stream of bytes that ‘looks random’, as in, there are no patterns to latch on to. This has tons of structure, not least the repeated 00s and ffs. I might have a go at it.
I didn’t see anything on there about what “passing” this challenge does for you in a concrete sense. I suppose it doesn’t guarantee you a job (or a visa since I think I would need one to work over there). Does it get you in the door to an interview?
The whole thing’s a joke. For a start, it’s not a cypher in any meaningful sense, and solving it requires you know the specifics of one particular brand of microprocessor. There’s no test of cryptographic skill. It just relies on people being able to recognise x86 opcodes.
No, you get taken to a congratulations screen with a link to the standard GCHQ careers page, urging you to apply.
There’s nothing new in this. Intelligence agencies, in the U.K., the U.S., and various other countries, have for decades been recruiting for new employees through advertisements in newspapers, at job fairs, by recruiters sent to universities, through websites, and by various other methods. The website in the OP may be a clever advertisement, but it doesn’t get you any closer to being hired.