Church tithing funds subsidize tuition which educates LDS youth regardless if there was an athletic program or not.
Athletic department revenues (ticket sales, donation, ad and tv revenue) pay for athletic department costs. Years ago, the athletic department had to borrow money from the general fund for a year or 2 but had to pay it back. Now, the athletic department is actually spending less than they're bring in. The athletic department is also working on setting up endowments to pay for most of the annual costs (eg building maintenance and athletic scholarships) with any new facilities built using donated dollars.