They're on athletic scholarships, how is that financial aid from the federal gov?
The federal criminal charge is wire fraud, which essentially means fraud that was committed across state lines. The claim is that the charged people defrauded the universities in question because the payments made the players ineligible and so the universities would not have given those scholarships were they aware of the payments. Additionally, they are claiming that the fraud deprived the universities of the control of their assets because granting the scholarships opened the schools up to potential sanctions from the NCAA. Finally, they tacked on money laundering charges since the participants violated those rules when moving the money in furtherance of the "fraud".
On the fraud charges, the defendants will have incentive to demonstrate that the universities were aware of and condoned this behavior and so there was no intent to defraud.
Fairly tortured way of turning this into a federal crime, but this case will get more attention than going after actual criminals and getting positive press coverage was the most important thing to the particular US attorney who started this investigation.