Translation:I am really happy that you liked my recipe.
Italian is more flexible on the use of "che" in relative clauses than some other Romance languages in similar structures (Spanish, for example). You will sometimes see instances where the "che" is dropped, like here. This is very common with the verbs "pensare" and "credere," for example. I would say, in cases of doubt, use the "che," since it is not wrong, any more than it would be wrong to say, "I'm happy that you liked," instead of, "I'm happy you liked."
The Italian subjunctive has a much broader use than just in counterfactual statements.
For example, it is used in dependent clauses after certain verbs of feeling, as in the DL exercise here.
There are similar patterns in English. For example, we say "If I were king" instead of "If I was king" because we are dealing with a counterfactual or hypothetical.
However, we can also say "It is important that he be there" instead of "It is important that he is there". Here "be" is a subjunctive in a dependent clause following the phrase "it is important".