I can't figure this out. I've tried just letting go of the rope and waiting for the chute to deploy, I've tried pressing enter mid-air, and then I've tried pounding away at every key, the desk, and whoever happens to be near by. Nothing works.

What am I missing?

You can't open a chute in the mid-air unless you're using TestStuff.
Normally this is done just by hitting a little the nearby wall while having it selected as a 2nd weapon.

While using a rope, fall against a wall gently and it should automatically deploy once you fall an appropriate distance after touching the wall.

Ah, it was driving me nuts. I can finally rest now. Thanks!

While using a rope, fall against a wall gently and it should automatically deploy once you fall an appropriate distance after touching the wall.

Assuming you have the parachute selected after deploying the rope