Question

How do the boys qualified as gentlemen of Verona as called by author

Answer 1

Bcz They Were Gentleman Hence they both were Dedicated to their sister

Answer 2

They're termed as gentlemen because they represented the following qualities of a gentleman:
1.) They were in a great need of money for the betterment in health of their beloved sister, but they never begged for it.
2.) Even after being so young, in the age where kids are supposed to play and being pampered, they're working hard, they're as selfless as to be called a gentleman.
3.) They never did anything wrong in the name of her sister, nor they tried any wrong job to get more money easily but unwisely. They're so gentle when it came to earn money.
4.) They're so respectful and polite that they didn't demand much from the visitor(sorry i forgot the name, 4 yrs ago i had this chapter), even when there was a chance of getting a lot of help.
5.) They wanted empathy, not sympathy, they refused to tell their plans to the visitor, because he might have sympathized the two boys.

There's no doubt they're young, but there's no doubt, they're the 'Gentlemen of Verona'.
Hope it helps. :-)