Jetting past someone is a different thing than trying to mug someone and there is also difference between trying to mug someone and trying to pickpocket someone. The piltover man probably isn't a complete lunatic, which you would have to be one to shoot at a person that sprinted past you.
The most likely and logical series of events in the comic is that Ajuna saw the piltover man and assumed he was rich or at least pretty well off, which is a safe assumption. He goes to pick pocket the man, maybe reaching for his gun side, maybe not. The man catches him and shoots him in the stomach. He seems to not have no remorse for what he has done because he looks outwardly relaxed as he whistles through the alleys. Ekko confronts him, questioning the piltover man aggressively. The piltover man responds with, "he deserved it", and while going into more detail, he pulls out his gun and fires at Ekko mid sentence.
From this we can see that he has little qualms about killing Ajuna and believes that he deserved it, most likely because he has some sort of prejudice towards people of Zaun. From a purely logical perspective, shooting at Ekko isn't too unreasonable seeing as Ekko had a weapon and you could even say that him shooting Ajuna was reactionary. If we were only showed one shot of the gone or the other, I would say that the Piltover guy wasn't that bad besides having an loose sense of morality and maybe being a little prejudice, but that isn't the case, one shot gives context to the other. Him making an un-reactionary decision to shoot Ekko, a fairly matured bodied male with a blunt weapon who aggressively approached him, makes the odds that the shot to Ajuna was reactionary much less likely. And if the shot against Ajuna wasn't reactionary, he made the sober decision that a young poor boy deserves to die for pick pocketing and had no remorse. This gives us the information to infer that he more than likely had other motives in his head behind shooting Ekko than, "Physically capable male with a blunt object is acting aggressive and frustrated towards me."
The piltover man at best is someone with lose morals, willing to kill young peoples when a small hint of danger comes his way and will have little remorse afterwards. At worst, he's an racist who believes that being from Zaun or being poor dis-values your life and is fine morally to kill those who fit those parameters, even a child. While Ekko isn't the most morally sound person in the world, the piltover man certainly isn't any better.