Looking for a movie about a game

The Wizard (1989)?

*Jimmy being the younger brother/character to Fred Savage's Cory.

hmmm.. nope. (can't quite confirm it but pretty sure)

The video game was not the central theme, it was just 1 of the tasks and it was an arcade machine not console/home TV, the game itself was (probably) not real, some kind of 1st person space shooter IIRC (I guess like the atari one? the graphics was not modern but pretty sure it was 1st person).

There *was* a girl AND an older boy on the team, and this kid (with a hat?) would just laugh at them from the back/corner of the store. Also, he was not one of the main protagonists. (but maybe he joined the team after that)

The footage had more 'quality', so pretty sure now it was 90's then.

Also, The Wizard features on the list I mentioned:
https://en.wikipedia.org/wiki/List_of_films_based_on_video_games#Films_with_plots_centered_on_video_games

Although I could be wrong about it not being there. (though not likely)
[thx!]

How about THE SANDLOT? It incorporated several "tasks" including getting the basebal back from a huge dog whose presence was a lwgend among the kids.

No. The kids were a little older, the scenery was not so much on the outside (though I can't remember the other tasks).
The "larger game" (meaning, the arcade is just an inner game) was like that game, I think in the US is called "scavenger(?) hunt" (not sure it is 'scavenger'), where each task give clues to where to go next and find the next clue.
Beating the arcade would give the next clue.