Alright, here's the deal:
For $20, you download Out of the Park Baseball 6. It's a baseball simulation computer game. Yes, you are the GM, and you can do all your own leagues and stuff.
However, these online leagues you see advertisements for, sometimes you do need to have OOTP to play, sometimes you don't. It depends on the league really. Usually, the leagues where you don't need OOTP are leagues where they use current rosters. The ones that are historical or fictional online leagues, a lot of times they require to use the game (via uploading and downloading files to update things, it's easier than it sounds).
So, no, it is not necessary to have OOTP play in a league. And no, even if you don't have it, you don't have to pay to be in a league or anything.
But, if historical and fictional leagues are up your alley, you'll probably need it.
Also, there IS a solo mode to OOTP, you can dynasties by yourself, if you wish.