Making a game Flash 7 compatible is - in most cases - a fairly simple process. Some of the most commonly used new features of Flash 8 are purely cosmetic, such as the filters, so a game doesn't depend on them to function. That said, to begin making your game Flash 7 compatible, remove all functionality that was introduced in Flash 8, Flash CS3, or any later versions that may come. These features include, but are not limited to:

When this is done, choose File -> Publish Settings. Click the Flash tab, then click the Version dropdown and choose Flash Player 7. Press the OK button. Now, whenever you export, your game or animation will be ready for play in Flash Player 7. Give it a quick play to make sure no functionality was broken in the process. That should be all!