My guess is that it's a paid service that needs to be reserved in advance, since the hotel is in the center of town, 15 km from the airport. Back in 2016 supatight80 said that the "Hotel limo service is a Mercedes Benz E class which costs 30 euros."

I would email the hotel for current prices (or to clarify the wording) but I can't imagine it's free unless you are staying in the presidential suite. You can also take the standard/official airport taxi (use the desk right outside of baggage claim for a fixed price that's 1800 Dinar [about $18 for the zone that the hotel is in]; don't go for people offering a ride). My guess is that the Mercedes is a lot nicer than the taxis I've taken but you have to decide if it's worth the difference.