How much air does my preamp need?

Not enough room your looking for trouble with that setup.

Heat is not a friend of any electronics equipment 

Do follow the manufacturers directions.   They didn't ask for a lot of space because it looks cool.   They know the more space they specify the harder it will be to include their product in some setups.  More ventilation is always better than less, so the manufacturers recommendations are a starting point but then there is not a critical need to exceed it either.  The critical need is to meet the requirements.

I'm guessing the manufacturers suggestion is probably a bit of overkill? In this situation I don't have a lot of choice. It's either an inch on top or no stereo in the living room. 

I am a guitar player and have used tube amps for decades. Many guitar tube amps are completely sealed with no ventilation at all and most of the rest have very poor ventilation and yet these amps can be used hard year after year or decade after decade. I've done many gigs outside in the heat of summer with only favorable results. Are stereo amps more susceptible to heat? How many tube preamps actually get 6 inches of space above them in the racks most of us use? What would be the temperature difference in 1-6 inches of clearance on the top? 

I'm not arguing just trying to get to the bottom of this because it is important to me. I do appreciate all of the replies.

If the sides are open it will be fine. I’ve talked to Pass and a couple of others regarding a similar situation I have running class A amps. If the front and back and sides are open, you will have no issues with overheating. A preamp, as mentioned, doesn’t put out much heat.