The rest seems like you have a bit of a chip on your shoulder about SJW types but I don't really want to get into that.

I do. But why wouldn't I? Let's say you love model trains. It's an expensive hobby, and you can only afford to buy a new train model here and there. So you go to TrainModels.org and look up reviews. You see a model get a perfect 10 review. Exciting, must be a great train model. When you get it, after spending your money, you find the quality very lacking. It feels cheap, and the wheels don't properly turn, cause it to derail if you try to put in on your track. So you wonder how it got such a great review. Turns out, the person doing the reviews is roomates with the person making the train model.
How would you feel about that? But that's not the rub. Here's the rub: When you send your model train reviewer an email calling foul on their shilled review, they don't deny it. Instead they insist that the fact that you care makes you sexist. What? What does sex have to do with this. You're talking about plastic train toys. Nope, you hate women. That's their defense of non-disclosure.

I've always wondered though, what the hell is "shillery"? I've only ever seen it thrown around by gamergate types and until now I've been a bit too afraid to ask.

I can provide examples if needed. But basically this:
If your website is covered in Kane Vs Lynch 2 ads, then it's going to look strange when you give it a great review. Especially when, by everyone else's standards, the game is terrible. So when the site gives the game a bad review, the game devs say, "well, why are we paying this site all these thousands of ad dollars to shit all over our games?" So they pull their ads and say "if you want our ad dollars, our games must get a score of X or higher." All this actually happened.
Who is going to give a better, unbiased assessment of a product: someone who is on a limited income and bought the game them-self and are going to review it because that's what they like to do, or someone who was given the product for free from the creator with a smile and a wink. If Site X continues to shit on every game made by Dev Z, then it's not very long before they stop getting those free review copies, and swag bags, and paid trips to cons.