No of course it shouldn't glow under normal conditions! Even when overloaded for an extensive period of time it'll usually get just barely too hot to touch. They also have a ceramic body filled with sand so except for the metal end caps I've got a truly hard time imagining one glowing red hot all over.
If you're careful you can open the fuse without damaging the ceramic part and insert whatever wire you feel like so that's one possibility what might have happened in that video. Lunatics have also been known to mill their own no-blow Diazed shells from solid aluminium or brass so I suppose one of those could glow if there was truly a short on a beefy supply but I guess that would require a few thousand amps.
I've got no way of knowing this but I strongly suspect that the fuse wire in Diazed fuses up to 35 A is exactly the same stuff you can buy on cards for your old Wylex fuses in the UK. Larger ones might be more tricky, I definitely know that German HRC fuses (called NH fuses, short for low voltage high capacity fuses) have pretty complex flat conductors with holes inside instead of plain round wire - we're talking 100 A and up, I believe the pictures I've seen were a 160 A one. These fuses are designed for incoming mains and DNO wiring, i.e. any place where seriously high fault currents can be expected.
Next time you see a video like this just hit Ctrl-C and give us the link, we're all curious!