"French is really beautiful!"
Translation:Fransk er virkelig smukt!
Reading through that (I really should have done that before), you're right. 'Virkelig' can be either adjective or adverb. The important thing they say for this sentence, however, is this: "som sætningsadv. kun: -". If it's a sentence adverb ([subject] er virkelig [adjective]), it's always just 'virkelig', never with a t at the end.
I like the other example, too. Det er "en virkelig(t) irriterende regel". :D