That clip is from A Trip Down Market Street, a 13-minute reel shot in San Francisco in the Spring of 1906, right before the great earthquake. It was shot from a cable car (identifiable by the cable channel running down the middle of the tracks) on Market Street in downtown San Francisco.

I'm not sure that it is necessarily an entirely accurate representation of streets before the widespread adoption of motor vehicle laws in the late 1900s/ early 1910s; I think the subjects of this film are being deliberately exhibitionist (most of the drivers in the film are driving loops around the trolley to stay on camera: you can see this with the drivers of the two White Steamers and the barrel-nose Franklin), so some of the more hair-raising parts of the film probably shouldn't be seen as typical.

Watching that video reminded me of an article I read recently: Murder Machines: Why Cars Will Kill 30,000 Americans This Year, which I think addresses some of your questions, and is regardless an interesting read.

According to the article, "In the first four years after World War I, more Americans died in auto accidents than had been killed during battle in Europe". Over 100,000 Americans were killed in World War I -- according to Wikipedia -- so over 25,000 Americans per year if divided evenly by 4 years, which I suppose is similar to how many people are being killed per year today by cars (30,000 according to the headline), except there's more cars and more people now.