I was there on a holiday a few weeks ago. While they told us that malaria isn't a problem anymore, they still warn tourists to protect against mosquito bites as they can still carry dengue fever. From a quick google it seems that malaria and dengue are spread by different mosquitoes, which might be why only one if the two is gone now.

Yep. Malaria is spread by Anopheles mosquitoes, while dengue, West Nile, yellow fever, and other Flaviviruses are mostly spread by Aedes mosquitoes.

In addition, Plasmodium (malaria) strains are much more species-specific than Flaviviruses. That is, while non-human animals can get a form of malaria, their malaria is usually not transmissible to humans. The Flaviviruses are much less selective (e.g., West Nile can infect birds as well as humans). This makes controlling the Flaviviral infections more difficult, as there's a virus reservoir in the animal population. Just wiping out the mosquitoes around humans isn't enough. You'd have to wipe out all the mosquitoes throughout the entire region.