"Time Lord" is not a race.
The natives of Gallifrey are Gallifreyans. That is their race/species. Gallifreyans are inherently time-sensitive, but they are not Time Lords. Time Lords are a small group of Gallifreyans with access to advanced technology that other Gallifreyans lack (this is muddied by whatever happened to make River Song whatever she is, but that's TARDIS magic and not relevant to a discussion of general Time Lord/Gallifreyan semantics; if you want the lecture, make it a separate question). They have a separate culture and look down on non-Time-Lord Gallifreyans.
Since we don't know anything specific about the events of the Last Great Time War, we can't tell whether the "civilians" in the Gallifreyan streets were Time Lords or ordinary Gallifreyans. It's hardly important, though, since you're asking why they don't behave like the Doctor.
The Doctor is a freak.
The Doctor left Gallifrey because he's nothing like the Time Lords. Time Lord law is strict about passive non-interference with history, and he couldn't stand by while people needed help. His active involvement and improvisational skills are what set him apart from his people. The Doctor is a rebel and a freak in his own society: smarts don't automatically mean courage or quick thinking.
Your average Time Lord doesn't have a sonic screwdriver, or a TARDIS; he's an intellectual philosopher-engineer living in a luxury gated community. When they caught the Doctor the first time, they exiled him to Earth. Later they manipulated him, exploited him, and used him to their own ends when they needed the qualities he has which they don't (or when they needed a scapegoat for their dirty work). Don't expect Time Lords to act like the Doctor. He left because they don't.