What's happening in this circuit? Zero voltage drop across dependent current source?
There's nothing wrong with having a short circuit across a (theoretical, ideal) current source, independent or dependent. (Similarly, there's no problem having an open circuit on the output of a voltage source, which is a good thing if you have some batteries sitting in a drawer somewhere) It just means all current from the source will go through the source instead of anywhere else in the circuit.

If you want to analyze this mathematically, and know how much current goes out port 2 (for example if you're trying to find the transfer function of the 2-port), you can put a resistor across port 2 instead of a short; then find the limit of the port 2 current as the resistor value goes to 0.