Oh dear....that's about the worst way to look at it, but yes. Goats are ruminants, like cows, sheep, llamas, etc. This means they have several stomachs, or more technically, two stomachs that are broke up into two. Actually, I think goats only have three. I can't remember.
What you are seeing is your goat chewing his cud. When goats eat the first time, their food goes into the first stomach. At a later time when the goat is able to kick back and relax, yes, he brings it back up (pukes if you will) re-chews it, and it goes into the second stomach, where it mixes with a second set of digestive fluids and bacteria. Usually late in the afternoon/evening, he'll bring it up and chew again a third time before it goes into the finally stomach and from there on into the rest of his digestive track. As gross as it may seem on the outside, it's an incredibly efficient digestive system that helps the goat maximize the amount of nutrients he gets out of everything he eats - it's a shame our horses didn't develop anything so efficient.
Anyways, a goat sitting on your porch chewing his cud is a relaxed, happy goat. It's a good thing!
Just as a side note, to no doubt gross you out further....you know how llamas spit? Technically, they don't - as in they don't spit saliva at you, they bring up cud and spit it at you. So, I guess really, you haven't been spit on, you've been puked on.
