Hi
My pleasure for the previous advice, unfortunately with regard to your staircase, nobody knows, or won't commit anyway!
The word on the street is that you need a license for anything using building products, that includes something as simple as tiling your toilet floor.
The danger in not getting the licence is in getting caught and denounced by an unfriendly neighbor.
As someone that has been through this horrid process I can advise that I am none the wiser now after many years of conversation with locals/professionals and I come with a legal/property history so I should have gleamed something by now.
However, this is how I see the rules so far on my trip up this rockey camino of building in Spain. Don't take my word for it.
In your position and with what you want to do, the enclosing of the stairs would be looked at as an amplification of the building (an extension). This is allowable if your property hasn't exceeded the allowed amount of construction that is allowed for the plot of land and the type of land your house is on. (urban gets more allowance than rustic (the equivalent to greenbelt in the Uk)).
Clear as mud probably but I have never been one for punctuation, spelling can be hard enough!
Oddly, a construction in timber is OK as it is deemed a temporary building, same with tents although these rules may have changed recently. One of the biggest problems with planning issues is the constant change in laws.
End of the day, it's up to you to decide but to do it legally you will definitely need a licence. Good luck with what you ever decide.