I've had a similar problem: the window was too tiny to fit a window AC unit.
The problem with portable AC units is they have only one pipe to the outside. A normal window AC unit has one airflow through the condenser, which is outside the room, and another airflow through the evaporator, which is inside. But the portable ones suck air from inside the room, blow half of it through the condenser and the other half through the evaporator, and throw away the hot air from the condenser outside. New hot air from outside has to seep into the room to replace the air that's blown out. So the AC unit blows cold air in your face, while hot air seeps under the door, and it's really inefficient.
So I got a portable AC unit that's roughly the width of my window, put it on a support so it would be at the proper height, and built a small frame stuck to its back so the evaporator fan sucks air from outside and blows it back outside.
This increases the efficiency to about the same level as a window AC unit, which is much better.
Oh, I forgot to answer the question. The reason they tell you to leave space around the device is to prevent it from blowing out cool air, sucking it back in, and blowing it outside. With the above, it doesn't happen.