Is there really no concept of low-cost airline over there? Or is it just an omission?
AzAL would probably not classify itself as a low cost airline, but offers very good rates to destinations in the region. http://www.azal.az/
There are several low cost airlines that serve the region. But keep in mind the Caucasus is quite a distance away from Europe, if that's where you're coming from. Meaning that the cost of flying there will be a bit more than for other intra-Europe flights.
Check http://airninja.com for low cost airlines that serve your destinations.
The list you mention displays low-cost airlines by their home country. This is in principle the country where the airline's headquarters are. For instance, Ryanair is listed under Ireland. This does not mean that the company only flies to and from Ireland. It has bases and destinations all over Europe and in Northern Africa. No entry for Azerbaijan merely means that the authors of this Wikipedia entry have not identified any low-cost company based in Azerbaijan. It does not mean that there is no low-cost company flying to Azerbaijan
Moreover, the concept of "low-cost carrier" is not precisely and unambiguously defined. This means that if you are asking several persons what a low-cost airline is, you will get several opinions. Anyway, it is only terminology. What matters is the price you have to pay for a certain service.
To get a more definitive answer, have a look at the homepage of Baku airport. There you will find a list of companies operating from there.