Learn Dutch: Het is grappig dat haar horoscoop precies heeft geklopt. - It is funny that her horoscope has been exactly right.

Yes, absolutely! Because this is a subordinate clause starting with dat, the verbs are pushed to the end. When you have a helping verb like heeft and a past participle like geklopt together at the end of a clause, you can choose their order. heeft geklopt (helping verb first) is known as the "red word order", and geklopt heeft (past participle first) is the "green word order". Both are correct and mean exactly the same thing.

I learned that kloppen means "to knock" or "to beat". Why does it mean "right" here?

While kloppen does mean "to knock" (on a door) or "to beat" (like a heart), it is also extremely common in Dutch as a way to say "to be correct", "to make sense", or "to add up". For example, if someone says something true, you can simply agree by saying Dat klopt! (That's right!).

Why is the adverb precies placed where it is?

In a normal main clause, the verb sits in the second position. But because the word dat introduces a subordinate clause, all the verbs are sent to the very end of the sentence. This forces other sentence parts, like the adverb precies (exactly), to sit right before the final verb group (heeft geklopt).

Could I use the simple past tense klopte instead of heeft geklopt?