I've purchased an Emirates flight, EK109, that states on my ticket has no stop, yet on closer inspection it actually flies DXB, LCA (Larnaca), MLA (Malta-Luqa). What's up with that? Do I get off in Larnaca?
What you have is most likely a "direct" flight and not a "non-stop" flight. Direct used to mean that there can be a stop along the way, but it's the same plane (and sometimes the same crew) and the same gate. That is still the case with Emirates and your particular flight.
Emirates has no non-stop between Malta and Dubai so you will land in Larnaca. Whether you need to get off the plane or not, depends on the specific route and airports, but they will clearly tell you when you land.
Other airlines have corrupted the term "direct" to the point where it has become useless. They simply combine two random flights and give them the same flight number. It's not the same plane, it's not the same gate, it's not the same crew and it is most certainly not a guaranteed connection.
Buyer beware and read the fine print.