Well the important thing to remember about that game is that it turned into more of a farce than one of the "greatest and most celebrated games". Kinda like those DIII schools that set scoring records by centering their offense on one player and play full-court press for the steal, and barring that allow uncontested baskets to get back on offense quicker.

But back to the point of the question, the NBA was not always the leading basketball league. It was a major sports league as throughout the 20th Century, baseball, football and basketball were the major sports (and the hockey fan in me wants to include hockey too, but I can't justify it). Just like the NFL was split between the National Football League and the American Football League before the AFL-NFL merger in 1970, so too was the NBA split in the 1960s when the American Basketball Association was founded in 1967. Un Just like the other scenario, the NBA was the established organization and the ABA was the up and comer. The ABA was able to attract key college talent and a few of the more exciting NBA players. The Boston Celtics were the dynasty of the 1960s in the NBA and UCLA was the dynasty of college basketball during that time. UCLA's top player was a 7'2" center then called Lew Alcindor, but now better known as Kareem Abdul-Jabbar. When he was being recruited professionally, a few sports writers mused that whichever league he chose would be the top league for the next decade. The NBA ended up winning the contest for Jabbar, but the ABA still carved itself a piece of the basketball pie.

But in the early 1960s, basketball was still gaining popularity. There were only 8 teams as of 1960. Across all leagues though, you'll see an increase in fandom and popularity whenever dynasties come into being. The Boston Celtics dynasty of the 1960s, winning 9 out of 10 championships in the decade, brought a wider fan base to the sport. Sensing public demand, the NBA started to relocate some of their teams to better markets and began new franchises. Ever wonder why the Los Angeles Lakers are called the "Lakers" despite the clear lack of lakes in LA? ^(totally unintentional tongue-twister there) They originated in Minneapolis, itself home to 20 lakes and in the Land of 10,000 Lakes. The price the NBA was asking for new expansion teams though was extremely high, which also played into the push for an alternative basketball league. It was only after the ABA's creation that the NBA rapidly expanded. The expansions brought the number of NBA teams up to 14 in 1968. The NBA's expansion strategy was not just one of opening up new basketball markets, but it was also an attempt to close the markets to the ABA. By 1974, the NBA grew again to 18 teams, adding teams in such basketball mad cities as New Orleans. /s

The ABA was able to thrive despite daunting odds because they were able to promote themselves as a different style of basketball. They added the three-point line to the court to add some more excitement and difficulty in shooting. Showmanship was the name of the game in the ABA and some of the rules were adapted to allow for that. The 3-point field goal was one of those. The slam-dunk was popularized in the ABA (not that it didn't exist before) and they included the contest in their all-star game in 1976. The ABA allowed for the drafting of college underclassmen, a shrewd strategy which was an attempt to kneecap NBA talent since the NBA didn't allow underclassmen to enter. They took their talent from places the NBA ignored. While NBA recruiting was focused on the urban centers of the Northeast and West Coast, the ABA noticed that there was a hotbed of raw talent in the South and Midwest which they capitalized on. They also had a longer shot clock which technically doesn't lead to an offensive-explosion, but it's not a perfect argument. The most distinctive feature of the ABA though was their patriotic red, white, and blue basketball they used instead of the orange one that is most common to us. While this style of play was very exciting and the league saw many new fans come out, they couldn't overcome the financial difficulties of trying to compete with the NBA, especially when they could not secure a lucrative television contract.

The two leagues merged in 1976 and the terms brought 4 ABA teams into the NBA (San Antonio Spurs, Indiana Pacers, Denver Nuggets, and New York Nets) and the other ABA teams folded. This merger brought the number of teams in the NBA up to 22. The NBA also adopted the 3-point-field goal, the more dynamic style of play, and the slam dunk contest in the all-star game. Today's NBA looks more like the ABA than the NBA of the 1960s. This competition, merger, and massive expansion were critical to the explosion in popularity of the NBA. Of course, this was nothing compared to the Larry Bird, and later, Michael Jordan era, but that's another topic for another day. Same goes for the 1992 Olympic basketball dream team, consisting of tons of superstars (...and Christian Laettner). There's also much more that can be said about the legal aspects of the merger, comparing it to the WHA-NHL and the AFL-NFL ones, but I'm not much of a legal scholar outside of some constitutional knowledge.

EDIT: Fixed a silly mistake.