Google's ngram viewer is helpful for beginning research on these types of questions.
The frequency has changed little in 100 years, so increased usage is not the cause. From ngrams, you can go on to book content searches for the time period of interest to study how it is used. There, we find sample usage such as this passage from Mark Twain:
Halliday's voice. “Fifteen I'm bid!—fifteen for the sack!—twenty!—ah, thanks!—thirty—thanks again! Thirty, thirty, thirty!—do I hear forty?—forty it is! Keep the ball rolling, gentlemen, keep it rolling!—fifty!—thanks, noble Roman!—going at fifty, fifty, fifty!—seventy!—ninety!—splendid!—a hundred!—pile it up, pile it up!—hundred and twenty—forty!—just in time!—hundred and fifty!—Two hundred!—superb! Do I hear two h—thanks!—two hundred and fifty!—“
Another example from The Importance of Being Earnest.
Gwendolen. Good! Algy, you may turn round now.
Algernon. Thanks, I’ve turned round already.
From these examples, we see there isn't a change in how "thanks" is used.
Without digging more, I couldn't say whether to the lack in Boardwalk is attributable to writing style or gangster mannerisms. Hardboiled pulp fiction will show how such characters and their speech were romanticized at the time.