"Sie mögen Tiere, einschließlich Katzen."
Translation:They like animals, including cats.
Yes, that works. Mind you though, "einschließlich" is a bit tricky, because it normally requires the genitive+article but there are exceptions to this rule (see here under "Grammatik"). It's one of those cases where you see and hear tons of poor-sounding grammatical constructions even from native speakers.
However, "genau?" isn't really used. Neither is "ja?" at the end of a question, which Hollywood uses liberally whenever a "German" turns up. We like to leave a bit more room for the possibility of being wrong, so the most common ways to ask "[...], right?" are "nicht wahr?" ("isn't it?", or literally "not true?") and "oder?" ("or?").
So "das ist richtig, oder?", or "das ist richtig, nicht wahr?" are much more natural-sounding. What you can also do is simply leave it out and re-arrange the sentence as a question by putting the verb first: "ist das richtig?" :)