The Times is a bit more circumspect, saying Trump "could have" used these losses to avoid paying federal taxes for "nearly two decades." In his campaign's response though, in addition to threatening legal action, Trump essentially conceded that he's paid little or no income tax, listing all the other forms of state, city, excise, property taxes and more that he has paid. In other words, everything but income taxes.
Needless to say, this alone would likely explain Trump's inflexible resistance to releasing his tax returns. It might well also explain and perhaps add credibility to Trump's claim that he's been permanently under audit for years. At least in theory there's nothing illegal or improper about what Trump appears to have done. The Times doesn't suggest Trump broke any laws. But the IRS would probably look very closely at a scale of declared losses which would allow a super rich person like Trump to avoid having any taxable income for decades.