How did "Columbo" manage to keep viewers engaged without the typical action scenes...

[TMC]

...like car chases and gunfights?

Question: How did "Columbo" manage to keep viewers engaged without the typical action scenes like car chases and gunfights?

Let’s see:

1. It was a “Howdoyoucatchem” as opposed to a “Whodunit?” type detective series - Columbo was different for 1970s television audiences as it would show the antagonist from the beginning and it would have Columbo (the protagonist) disassemble the alibi that the antagonist was using to obtain a confession. Many of the individual episodes were well-written and that certainly helped audiences overcome their natural inhibitions about being told the “mystery” in advance.
2. Peter Falk was an exceptional actor - He WAS Columbo. Even though Falk had dozens of roles prior to Columbo, he walked into the role and inhabited the character. As noted in another answer, Falk’s performance is likely one of the reasons that the series has not been rebooted. Yet.
3. The series cast exceptional actors as the antagonists - While they overused Jack Cassidy (see below) and Robert Culp, both men were exceptional performers as were the overwhelming majority of Columbo actors cast. Watching the nominal villains was often the “next best” part of the series to watching the man himself.
4. Southern California itself was the star of many episodes - It may seem odd to many people today, but to those living in other parts of the United States, Southern California was still pretty “exotic” in 1970s. The episodes that showed the mountains, hills, deserts, and huge estates took viewers places that many wished they could visit, but didn’t. Los Angeles/Hollywood was a magical place back then and setting Columbo there as opposed to New York City or somewhere helped the series immensely.
5. There are “just enough” Columbos - There are 69 episodes in total of the series and its 1990s ‘update”. That’s just enough Columbo for audiences to enjoy the character without him becoming too dull or predictable. One of the major problems with North American television is that too many series made too episodes and so “diluted” their characters. Had Columbo been a 22–27 episode per season series, it’s likely that it would have been canceled after its second or third season as audiences would have grown tired of the character and the narrative. As it was Columbo was only of the series on the “wheel” (NBC Sunday Mystery Movie) that has survived in the memories of viewers as the other series simply wore out their welcomes with viewers.

Columbo didn’t need car chases or gunfights querent as it was considered to “adult” entertainment at the time and as such it somewhat “highbrow”.