Warning!! I am not a product safety specialist or lawyer. I take no responsibilities for any error here or any gaff you may make concerning the CPSIA
The Consumer Product Safety Improvement Act is a federal law that requires that a variety of tests and compliance certifications be made before manufactured toys and games can be sold in the United States. Products that are affected are those that were designed or intended primarily for children 12 years of age or younger. The CPSIA includes a variety of testing requirements, but is particularly concerned with lead content in manufactured goods. Packaging which is intended to be disposed of (like shrinkwrap) is exempt, but even includes testing of small plastic bags if those are designed to store game parts for later use. If you are in luck, your intended manufacturer certifies everything they work with, potentially making testing a little cheaper. Chances are, however, you'll eventually get hit with a bill for testing somewhere along the way if you make products intended for use primarily for children.
These tests do not apply to products that are not intended primarily for children. So, for example, if you develop an abstract strategy game primarily intended to be played by adults, then you could be exempt from CPSIA testing. It is not as simple as just saying your product is intended for an audience 13 years and older. The totality of the product, its packaging, and its marketing can be considered.
Particularly if you are manufacturing overseas, you will want to make sure that your manufacturer and importer know the CPSIA requirements and can issue appropriate certificates. You will have to plan ahead, even if you manufacture domestically, however, because packages have to bear special information required by the CPSIA. Such information cannot merely be added on after the fact as a sticker.
This is the kind of thing you may want to buy some time with a lawyer or product safety specialist to discuss if you have any doubts about the CPSIA knowledge that your manufacturer and/or importer brings to the table.