Based on what I've read I thought I was supposed to drain the pool to 4" - 5" below the skimmer and then winterize (add chemicals). I just received my winterizing kit and it tells me I should add the chemicals while "circulating pool water". Am I supposed to close the skimmer valves and leave the main drain valve open and run the equipment or just add the chemicals before I drain the pool?

As with any chemical addition, you need circulation to disperse the chems throughout the water. If you can do that after you drain then that's how it should be done. If you have no way to disperse them once the level is below the skimmer your best bet is to go ahead and add the chems, circulate, then drain. So, yes run the main drain only.

Most of the ingredients in those "kits" are unneccessary, just an FYI.

All I have used for the last three years is chlorine - and I open to a Trouble-Free Pool, with a FC residual.