Why isn't NH3 an Arrhenius base? And why isn't HCl (g) an Arrhenius acid?

According to Arrhenius theory an acid : is a compound that produces (H+) when in water. And it is said that one of the things against Arrhenius's theory is :- e.g:- in HCl (g) + NH3 ----> NH4Cl (HCl) is not an Arrhenius acid , because there are no ions. What I don't understand is : Did Arrhenius say that the acid must be in the shape of ions while it is reacting, or did he just say that if we take it (not necessarily while it's reacting) and put it in water it is going to produce (H+) ? The same thing goes with (NH3) , if we put it in water it is going to : first change into (NH4OH) and then (NH4+) and (OH-) ,,, so eventually it produces (OH-) , right? So why isn't it an Arrhenius Base ? Or did he mean that it must be able to produce the ions directly without changing into another compound first?