Japanese has two different ways to say "and". For multiple nouns, they use a separate word just the way we do in English. For multiple verbs, they conjugate the non-final verbs a particular way.
I imagine DJP took inspiration from Japanese, but flipped around where to apply which technique. Multiple nouns are declined a particular way. "Thank you" and "hello" are not nouns but pleasantries, therefore declension does not apply to them and a different technique must be used.
According to the Dothraki Wiki, kirimvose is the instructive of kirimves, meaning happiness, which again comes from the word kirine (which I am sure you know by now), and the derivational suffix -ves, which turns adjectives into abstract nouns, much like the English -ness. Rytsas comes from the word rytsa, meaning healthy.
I'd like to think this is how HVers usually greet one another. I don't know of any other languages that thank people immediately, unless it's "Thanks for coming. Thanks for choosing Brandname. What can we do for you today?" I can now do customer service in HV! "So why were you fired from the call center?" "Um, it's a long story."