I appreciate the extra info but you missed my question - what would you call these? These are all items that we commonly see out in the world, and close to 100% of people understand them to mean that no currency changes hands but someone, somewhere, somehow pays for them. What would you rename these to, given how resistant you are to even some guy on a forum saying that a website is free to view, in a way that's consistent with this universally understood meaning?
Three of them are clearly advertising, which is a form of payment. For something to be free, there must be no expectations.
Expectations are what you give in exchange for something else. Currency can be US dollars, or it could be the Euro, or a Pound. And using an exchange rate they can be evenly changed from one to another. Right now there is an expectation that for every 6.18 in Euros you will get $7.25 in US dollars. But both of those can be turned into 1 hour of US federal minimum wage payment. One hour of work in the US is equal to 6.18 Euros.
It's that expectation that is important for distinguishing if something is free. Currency is just a way to assign numerical values to different things to make payment easier but you can pay for things with something other than cash. You can pay with eggs, 8 hours of pushing papers on a desk, or 30 seconds of staring at a screen. We often pay for things by giving them a portion of our life in the form of attention. Generally, the party that sets the conditions of cost is the one who gets paid.
Amusement center prizes cost tickets, not cash, and I hope you wouldn't say that every item behind the counter is free. You pay with tickets. For a child who earns those tickets the cost is the time necessary to get them. Sure, cash might be involved, but it doesn't have to be. I used to have an arcade that gave tokens for each book you read. The tokens weren't free, because you had to read a book to get them, and the tickets weren't free because you had give the machine a token and your time and energy to get the tickets. And the prizes weren't free because you had to give up tickets to get them.
I suspect you are confusing me being wrong with the people you know not considering what they had to spend to get so-called free. Just because someone says something is 'free' and doesn't charge money doesn't make it free. There are a lot of things people use the wrong word for, and while most may typically just roll with it, that doesn't make their use of term correct. For example, I can't tell you how many people have told me their dog just gave birth to puppies despite the fact that no dog in history has ever given birth to even a single puppy.
I am stuck on this because it's a peeve of mine. We so badly want things to be free that often we just start using the word when it doesn't apply. And maybe it's just another example of how language can give us words that mean the opposite of what it means (such as literally). But while literally is annoying misusing free actually impacts the way people perceive the world. It changes our conception of fairness and rights. So for me, calling something free, when it isn't free, harms us.
So... I am sorry if I may have come off moody, but free means something.