All the free game sites package a low level adware package with their installers, so that when you run any game from their sites it will usually start with an advert while the game is booting up. This can take between 10 to 30 seconds to complete before you can access the actual game. Also, when you close the game down, your browser is opened to the distributors web site.
These activities are not malicious and earn the distributor money (via the advertising). Part of that income is shared with the developer of the game you downloaded for free. Developers can earn a lot more money; especially from their older games, than from sales of their games simply by allowing their games to be given away for free. Basically it's a Win, Win, Win,Win for everyone i.e. the consumer, the distributor, the developer and the advertiser.
Most free game sites such as Falcoware Games, MyPlayCity, Gametop, FreeGamePick TooMky Games, and others use this method. Most of the games given away in this manner are actually commercial games and not freeware. You'll find most of them on commercial sites like Alawar, Big Fish, Steam, Gamersgate, Gamehouse, GameFly Direct2Drive, Game Fools and others. (though not all game distribution sites that offer free games include adware installers for example Itch.io, Good Old Games, Epic Games and Steam all offer totally free games with no advertising. These distributors have a generous number of totally free games; that said, Steam and Epic Games also have a selection of Free to Play games that also include in-game purchases or paid for DLC packs that although not necessary to play the base game, are often essential if you want to actually progress or survive enough to enjoy playing the game without having to spent countless hours farming for materials etc.
For example:One of the first free to play games I played almost a decade ago included paid for DLC packs. Your free to play character had no armour and the only weapon available was a low level pistol. I played without any extras and for almost an hour was killed countless times and never once managed to kill an opponent. There was one time where I managed to stealthily creep up behind an opponent who was obviously using paid for armour and weapons and I emptied almost a full magazine of pistol rounds into his head, whereupon he turned around and shot me once and I died instantly. I promptly deleted the game.
The low level adware packaged with all these games given away is specific to the game, i.e. it is installed inside the games installer and will not affect your computers system whatsoever. i.e. no advertising popups or other actions not allowed by you will occur via your system, only via the games you've got from these sites and only when you boot up the game; no malware is installed to your system. When you uninstall the game the adware goes with it.......
To reiterate, the adware installed within the games does not damage your computer, corrupt files, install Trojans, steal sensitive information or allow others to access your computer or network. The advertising you see is there only to earn the distributor and developer some money for allowing the game to be given away for free