Dick's can deny sale or service to anyone they like. It could easily be perceived as age discrimination and it's a legit stance.
I see this repeated a lot but if you run a business that way, especially retail or otherwise dealing with the public, you are constrained in what you can do regarding customers or risk being sued and/or fined by the government.
For example, Dicks and other retailers do not have total liberty to pick their customers--the federal government and states, counties, and municipal governments have what are called public accommodation laws. These especially apply to retail stores and forbid discrimination involving customers on a whole host of issues. The obvious are covered by the U.S. Civil Rights Act which allows those who were discriminated against to sue the establishment (Heart of Atlanta Motel Inc. v. United States, 379 U.S. 241 (1964)). Another group of customers is covered by the Americans With Disabilities Act. But states and localities have their own anti-discrimination categories as well and these have generally been upheld by courts. For example, California bans discrimination based on political opinion which may get Google into trouble with firing James Damore.
Age is one of those weird categories that is protected in some cases and not in others, depending on the circumstances so an eighteen year old MIGHT be able to sue depending on the wording of the law if the purchase was otherwise valid under state and federal law. However, it might be valid as I seem to remember car rental agencies often have refusal to rent based on age. Too lazy to read up on the caselaw and statutes right now and a lot of it may depend on your state and locality as well.