"Cities" don't make a decision about what to base their economy on; for various reasons, different business enterprises happen to prosper and grow in different cities. For much of the 20th century, Nevada was the only state to allow open gambling, so Reno (closest city to San Francisco) became "The Biggest Little City in the World." During the 1930s, trade from the Hoover Dam construction workers at nearby Boulder City caused Las Vegas bars and gambling establishments to grow, and after World War II, Las Vegas's proximity to rapidly growing Southern California allowed it to surpass Reno's importance.

It's worth noting that most of the Strip is not actually within the municipality of Las Vegas.