Frames have nothing to do with storing information.
Using frames can be one method to create an area on each page of the game. Frames are often used for the menu. Current browsers support frames, but the HTML <frame> tag will not be supported in HTML5.
Another method can be the HTML <div> tag, but using this HTML tag is for persons with not so good HTML knowledge more difficult than using frames.
A game creator should use the method which he understands and he can code in HTML.
If a game creator only knows how to use frames, he can either create a game with frames or he can“t create or finish the game.
Dating Ariane is an old game with many pages. The first version of the game came out twelve years ago. It was created by using FrontPage 4.0. Perhaps, when the game creator started to code the first version of the game, he had decided, because of some reason, to use frames in Dating Ariane. After finishing so many pages he cannot switch the game to a game without frames because if he wants no frames he had to change all pages.
I personally prefer games without frames, because of several most personal reasons.
I still remember the time when not all browser support frames and I learned HTML a short time before frames were seen as evil.
If I change the size of the browser window showing a web site with frames, a scrollbar appears somehwere on the screen.
I personally respect sites which are good programmed. Using the HTML div tag is for me personally better programming than using frames.
I am not an native English speaker, so if you find some mistakes in my English, inform me, so I can correct them and improve my English.