The answer is, unfortunately, that Driver:SF tries to authenticate itself with the Ubisoft UPlay servers every once in a while; if the UPlay servers are down or not responsive (e.g, there's a big sale going on at a major video games retailer), you'll experience random pauses like in the video.
The way to fix it is to either disconnect your computer from the Internet entirely, or block Driver: SF from the Internet at your firewall. Doing either of these will make Driver: SF's authentication fail fast enough that you won't notice any pauses (except in cutscenes, where the dialog will still drop out every once in a while).
Here's how you'd block Driver: SF on Windows 7. Doing so on Vista or 8 should be similar, and you can find guides for XP:
1. Open the Windows Firewall Manager
2. In the window that opens up, select Outbound Rules and then New Rule...
3. Leave Rule Type at the default (Program) and click on the "Program" link to the left, then enter in the path to Driver:SF's Driver.exe file. For most people it'll be in
C:\Program Files\Steam\steamapps\common\driver san francisco\Driver.exe, but I have a weird configuration.
4. Hit next a couple of times to default to blocking Driver: SF all the time on every network, and then give your new rule a name. Feel free to vent. Then hit Finish, and you're done!
Note that doing this will keep Driver: SF from ever going online, which means no multiplayer, no UPlay points, and I believe no Steam achievements if you're into that kinda thing. However, it does mean that you can still play the singleplayer while the summer is young and the deals are fresh.
Later on, once things have quieted down and Ubisoft's UPlay servers aren't a smoking ruin any more, you can let the dogs out and get all your sweet Internet points by deleting the rule from the Windows Firewall window:
And now you are a fully-certified Windows Networking Technician. Good luck.