Income Tax Expense is not just Federal - it's any income tax, which for Nike includes State and Foreign taxes. If you look at Note 9 of the report you'll see a breakdown in which their federal income tax is actually negative, which may be how they ended up on the NY Times list.
In addition, income tax expense does not necessarily equal income tax paid. Companies have various ways of deferring income tax so that it's accounted for in one year but actually paid in future years. So even a company with a positive income tax expense may not pay it until future years. Whether the NYT criteria is tax accrued or tax paid I have no idea (and don't care) - it's behind a pay wall.