The most common reason you may need safety testing is if you plan to sell your books or games to a young demographic through a retailer. You will need to make sure your product meets safety requirements designated by each country.
The most common safety tests are done to verify that a printed product meets all requirements of the CPSIA (Consumer Product Safety Improvement Act) in the USA.
However, for games, additional testing may be done to verify that a game is suitable for specific age groups. Without testing, games can only be labeled for ages 13 and up. Games that will be sold in Europe may also want testing to verify that their game meets CE marking requirements.