Question

how do the boys qualify as gentle men of Verona as called by author

Answer 1

Both the boys work really hard to provide for their sister although they're both very young. Their determination and hardwork is commendable. Also they first politely refuse the narrator when he offers them a ride to their sister's place and only accept upon the narrator's persistence.

Answer 2

The singularity of purpose and capacity to work hard of nicola and jacopo greatly  impressed  the narrator . They had all great qualities of a gentlemen like love, dedication, honesty etc . That's  why  the  narrator  called them as "THE TWO GENTLEMEN OF VERONA "