I’ve been playing and designing games almost all my life, and playing published roleplaying games since I was 11 years old (and unofficial ones before that).
I’ve heard some people try to make the case (or just assertion) of that definition (or similar definitions, such as “some things have higher value than other things”) of what a game is, and I would say they are annoyingly trying to impose too narrow a definition of what a game is. Roleplaying games in partictular are quite often played without clearly-defined goals, and with the real goals being to enjoy oneself, to have the experience of shared imaginary worlds, or to experience or explore situations of interest.
I think people who assert that they know the “necessary characteristics of a game” and specify narrow things like that are wrong and annoying.
As for eventually growing out of them, they’re also wrong and annoying about that too. Many people have played RPGs since they were first published as such, and many people have died in their 70s-90s while still being active roleplayers and/or developers of such games.
Again, people who write those things are wrong and being asses.
Also, RPGs can and often do have objectives and scores. But those things are optional, and it’s often said that the real goal is to have fun. Players of such games discover things about what they find fun, and that different players have different ideas about what they want from games. (Unlike the ass-hats who write that RPGs aren’t games.)
Because RPGs have so many different games, styles of games, styles of play, different people running and playing the games exploring what they want to do, and different individual sessions, there is a vast variety in what people do. There are some popular conventions, but those are by no means the best or only ways to play RPGs. To use such an example would be like saying whatever the most popular corporate pop music style currently is, is the way all music is done.
One example:
An experienced player wants to introduce other players to one set of RPG rules. He invites a group of players to come play. They’re told the game will be an arena combat (q.v. Spartacus or Gladiator) and asks each of them to pick from a list of pre-made characters who have their ability ratings and equipment listed. Then he has them choose who is on which team, lays out a map of the combat arena with pieces representing their figures, and guides them through the process of play, asking them what they want to do each turn, explaining their options and how the game determines what happens, and the battle is played out.
Another example:
The host (or “Game Master” (GM)) has developed an entire game world with maps of locations and hundreds of characters and cultures and situation details (or purchased a published one, or some combination of purchasing and inventing). He represents the narrator. The players have designed or chosen various types of characters who they each represent, and personalized them, and developed them through many sessions of play. Play consists of the GM describing the current situation, and the players saying what their characters would like to do, and acting out various conversations between characters in the game world. When some situations develop, there may or may not be various rules systems which determine (or suggest, or help determine, along with GM discretion) what actually happens, often including detailed combat as the group in the first example were playing. The situations can involve all sorts of things. For example, the author of Game Of Thrones plays the Generic Universal RolePlaying System (GURPS, one of the two RPGs I prefer), and the action in those books bears some resemblance to some RPG play, which could include any of the situations seen there.
There are very many other types of example, including LARPS (Live Action RPGs) and styles that are more like improv or collaborative storytelling and/or worldbuilding. it’s an endless topic.