Do they have to pay Adobe if they use Flash to animate? Do they have to give them money in production, broadcasting, or otherwise?
As a media creator, you pay for use of the tool, not for the use of the result from using the tool. Different companies have different systems, but you either buy the software up front or pay a fixed subscription to have the tool available to you.
It does not matter if you are using it for personal use (though sometimes educational copies will get you a discount for non-commercial use), making a video for your ad supported youtube channel or producing the super bowl. The cost of the software remains the same.
It's similar to buying any other tool (say a hammer). You can either buy the hammer or rent it from a hardware store, but you don't pay for every house you sell that you build with the hammer, you just pay for the hammer.
Once you bought a license for the software you are good to go. In case of Adobe you simply subscribe to the Creative Cloud. There is no royalties for the usage of software, like for the usage of creative content like video or audio footage or images from other artists.