Under United States law, fantasy sports games and computer games have a right to use team and player names and statistics, protected by the First Amendment to the United States Constitution, and no license is required to enjoy this right.
This right was unambiguously upheld in the case of C.B.C. Distribution v. Major League Baseball (United States Court of Appeals for the Eighth Circuit, 2006).
Major League Baseball appealed to the United States Supreme Court, but were denied a writ of certiori, leaving the 8th District Court's ruling as the law of the land.
I am not a lawyer. I just know that we have followed that ruling for the last 9 years, and our own legal counsel strongly affirms that we are well within the law.