Terms & Conditions of a website, even a government website, aren't law.

INAL, but guessing they're technically contract law.

It seems like it's not. Nobody has ever prevailed in court for the "you can't deep link to our website" clause. There is a circuit split on "you can't embed images from our website". In the 9th Circuit, Perfect 10 v Google establishes precedent that you can <img src="someone else's site"> if you feel like it. In the Southern District of New York (2nd Circuit), Nicklen et al v. Mashable, Inc. defines precedent that you can't. As far as I know, the 2nd Circuit Court of Appeals has not said anything about that. Either way, the next person to encounter this issue probably goes to the Supreme Court.

I think the department of transportation is overreaching. You can link to the location of the traffic cams and the video feeds. If they want to make that information private, then fine, they might be allowed to do that. But telling people about something that's public isn't illegal. That people are disrupting traffic by standing in the street having their pictures taken is too bad. They can increase the refresh rate to avoid that problem, or they can remove public access, or they can have the cops write people tickets for blocking traffic. Of the cameras in my neighborhood that I looked at, most of them can take your picture on the sidewalk and all of them can take your picture in the crosswalk during a walk signal.

Overall, I get why the DOT doesn't like this site, but I think it's kind of too bad for them. The DOT wants to maximize vehicles per hour. Residents want to take back their streets. Sorry, DOT. Evolve or die?

They are not. Or rather they have generally been deemed unenforceable as such (at least in the US). You can, of course, be banned by the service for violating them.

This is similar to signs regulating behavior that businesses might put up. By and large those are not in any way legally binding. Generally all the proprietor can do is ask you to leave. But since they can and often do ask you to leave, people generally abide by the posted requests.

In a similar vein "not liable for THING" signs are more accurately read as "we don't wish to be liable for THING and are going to attempt to refuse if at all able".

Without an exchange of money (or goods), there's no contract between the parties. Other laws may apply such as copyright, but not contract law.

which law is being broken here?