If I make a review with a game I won here, should I apply the "Product received for free"?

It's up to you whether you want to do that or not :)

I think it should only be used if the developer gave you the key in exchange for a review.

You don't need to. But you could write that you received it as a gift from a friend. That may help clarify the question of value for money for some people.

IMHO, I would.
Because as a reader of reviews, contemplating the purchase of a game, I would want to know if the reviewer is biased one way or the other based on the impact to their wallet. (If, for example, I read a review of Null Person's Atmosphere and a person says they absolutely loved it, but doesn't disclose that they didn't pay anything for it, it colors my bias as a purchaser towards thinking it's worth spending money on.)

Also yes, I would state something about where you got it from -- that it was not a developer-provided or game review press key.

It's up to you and there is no one definite answer to that.

I never do. Somebody actually spent that money to deliver me a gift, so in the end he did not obtain it for free, and whether or not I win a game on SG or spend my own money, I feel exactly the same about the game. However you can as well take other side of the barricade and claim that whether or not you spend your own money influences the review, so marking it for all your SG wins is not a bad choice either. Another option is using that mark for dev keys only, but then again, it's not always obvious whether the key was bought or obtained/generated for free, so there is that.

Just stay consistent.

For transparency's sake, i would say both mark it as free and detail that it was a gift from a friend, group, website, or developer. If you paid or traded a meaningful quantity of valuable objects for it, then i'd say you're probably off the hook on that one.

The problem is that there is always a value proposition to be had when it comes to assessing things. Take a chocolate bar for instance; Nearly everyone loves a chocolate bar, especially if its free, but if you have to pay $100 for an off-the-shelf chocolate bar you're going to have vastly different opinions and expectations of it. Granted money is valued differently depending on the person, but people are much more willing to overlook small flaws in a cheap or free thing than they are in something that they paid a lot of money for. Additionally, the more information readers have when they view your review, the better off they are. If you felt it was a little expensive, or that you got a bargain, thats also a useful metric in helping to judge and interpret the tone of the review and the mentality of the reviewer as they were writing about the game.

I never use this marker on any of my reviews, even if the key is from a developer for a review. Why? Because I put a lot of work and effort into writing my reviews and it will never be "for free". It takes me a lot of time to play the game, to analyse it, do a comparison with games I played and so on. Thats gaming experience you can not "buy". But I must say, that I am going to give an recommendation about the price of a game. So if its not worth buying for full price, I say that ppl should wait for a sale and normaly I take a look at the historical minimum at isthereanydeal. People can work with this information way better than with the flag "for free".

Most suitable interpret that checkbox as "I received this game free through means that would bias me toward a favorable review".
While that's normally exclusive to developer/publisher-provided keys given out for review (as there's a threat of lack of continued keys from developers if you give out negative reviews, which would bias you toward avoiding giving such) if you personally feel your review isn't as judgmental as it would have been had you purchased the game on your own, then it could also be considered suitable to check the box.

Most of the time, however, that's completely unnecessary, as we all purchase games at wildly different prices when reviewing them, anyway, so our perspectives on that always differ (and should, if necessary, be noted within the review- eg, "This game isn't worth full price, but I was satisfied with it at the bundle price I purchased it at."). Past that, the way I see it, if getting a game for free devalues it in any way whatsoever, then it's probably best to take a close look at the games you're trying to get a hold of, and see if you'd be as interested in them if you had to pay for them yourself.

If I receive it for free, I'll note it. Gift from friends is also free in my book.

no. a review is a review, steams attempt to dismiss reviews that it didnt recieve money for from the reviewer is pathetic.. dont buy into it, just review it as normal.

Yes. The checkbox says you should mark it if you received the product for free. Did you pay for it? No? Then you received it for free.
I understand where you are heading with that question, but sometimes simply following the indications is the most correct way of action.

I wouldn't check it if it was something I won from SG, or got as a gift from a friend. I read it more like "Did the developer get money for this product due to you having the game?". The point of it is imho to determine if you got a review copy or not.

As long as someone paid for it, even if it wasn't me directly, I wouldn't count that as "free".