Lines 113-116 Summary

Get out the microscope, because we’re going through this poem line-by-line.

The Whore & Gambler, by the State
Licenc'd, build that Nation's Fate.

Although Blake had liberal and radical ideas about a lot of things, he apparently wasn't a huge fan of prostitution and gambling. He was fairly religious, after all.
Blake's other poems (see "London," for example) indicate that he saw prostitution as something that was forced on women by poverty—it wasn't a fun career choice. The government licensing prostitution just shows that the government tolerates poverty and doesn't want to work against it. The same goes for gambling—instead of giving people good jobs and a decent economy, the government just gives people more opportunities to get addicted to gambling and throw their money away.
By tolerating corruption on a small scale, with gambling and prostitution, the nation builds a corrupt state for itself. You could argue that this is a "world in a grain of sand" thing, since Blake takes a small example of something and says that it's going to affect the country on a bigger level. Little corruption is big corruption in miniature.
(You could interpret these lines as saying they opposite—if you license prostitution and gambling, they'll become a decent part of the economy, which will help build the nation's fate in a positive way. But, peeking just ahead, the next couplet makes it clear that that's not what Blake means…)

The Harlot's cry from Street to Street
Shall weave Old England's winding Sheet.

Blake's saying basically the same thing he was saying in the last couplet. Prostitution—or the exploitation of poor women by richer men—is a symptom of a nation's destruction.
A "winding sheet" is the sheet wrapped around a dead body when it's being buried—so "the Harlot's cry" is going to wrap "Old England" in the same way and prepare it for its doom.