Ramming them while he's on a bike too would have been a terrible idea as he'd have come off too. He did the right thing by just following, tracking them until they dismounted either intentionally or otherwise.

Like others said you cant really ram someone on a bike.

The game is just to keep pressure on them until they make an error, which they did.

When they're zipping through those tiny alleys it was inevitable that sooner or later theyd get blocked in or have to climb some stairs or something.

Way back when I was in school a kid tried ramming me on my bike with his, he learned very quickly why that's not a great idea. The rammer will completely lose steering and end up ass over tea kettle the second his front tire touches the other bike. The other bike will be fine unless you also get his front tire, in which case you both will go down.

Only thing the cop could have done is get in front of the other bike and cut it off, hitting the other bike's front tire with his back tire. That would keep him stable and cause the other guy to bite it, which is very dangerous to even try and can really go wrong quick.