You have also probably seen this put in the context of those who recall Newt impeaching Bill Clinton for... yup, "obstruction of justice." The hypocrisy shouldn't surprise you. That case was about an affair with an underling, and Newt was, himself, having an affair with an underling at the time. The tradition of thought here goes back to, of course, this little gem...
And now, I can't believe I'm going to post this, but...
Newt Gingrich is reaching back to the Nixon defense (or forward to the Judge Dredd defense), and not by accident. Trump did the exact same thing that forced Nixon from office. Well, not the exact same thing. Nixon kept his tapes secret because while Nixon was paranoid, he was smart. Trump is the dumbest motherfucker in political history, so he blurted out his own guilt on national tv. The only defense is the Nixon/Dredd defense.
There is even a semi-coherent theory behind it. During the Bush 43 administration, you may have heard of it as the theory of the "unitary executive." It is the notion that all executive power is vested in the president. No member of the executive branch has independent authority beyond what the president allows-- including the Director of the FBI. Thus, the president is in charge of all investigations, including investigations of himself. Thus, there is literally no way that the president can obstruct an investigation. That is the obviously-hypocritical argument that Newt was making.
The hypocrisy brings us to Miles's law: where you stand depends on where you sit. Executive authority is a tricky kind of issue, and most people don't really have coherent preferences on it. If they like the president, strong executive authority. If they don't, weak executive authority. So, would Newt have accepted anything like the unitary executive model or an "I am the law" argument from Obama? Hell no. He didn't from Clinton, and that was about a lie about a blowjob while Newt himself was cheating on his own second wife (he had left his first wife while she was convalescing in the hospital from cancer, and he was, shall we say, not diligent about paying child support because Newt Gingrich is in competition with Trump for most vile sack of festering, disease-ridden bio-waste in modern political history).
Process arguments and outcome arguments are difficult for simple minds to grasp. Making a process argument requires accepting that the argument will cause you to lose at some point. Nobody likes to lose. Accepting a process argument requires accepting the rightness of your own loss, once in a while. For Trump, you can see why this is a problem. He defines everything in terms of winning and losing. No loss is legitimate to him, so he can never accept a process argument. He'll lie and cheat because all that matters is winning. Newt is the same way. He is, historically, Trump's progenitor.
He rose to the position of Speaker as the guy who would do anything to win. For 40 years, the Republicans were the minority party in the House of Representatives. One faction-- the Bob Michel faction-- basically accepted that, and was willing to go along and get what they could for their own districts. Gingrich led a faction that came to be called "the bomb-throwers," whose mindset was to tear down anything they could, obstruct everything and fight tooth-and-nail based on the premise that the only thing that mattered was trying to get majority status, by any means necessary, so to speak. Nothing was out-of-bounds for Newt and the bomb-throwers. In 1994, they finally got control, but since Newt is a total fucking moron, the 1995 shutdown, the impeachment and Newt's own ethical problems led to his own downfall in 1998. Still, Newt set the template for Trump, and his Miles's law interpretation of executive authority? Yup. That's there too.
Trump, of course, knows none of the history, none of the law, and nothing about anything. The famous line about Newt Gingrich (the origin of which is difficult to trace) is that he is a stupid person's idea of a smart person. Trump is just a stupid person, but he is the reductio ad absurdum of Gingrich, and Newt was already absurd.
Trump, Newt and people like that have neither the intellectual nor moral capacity to make process arguments, like arguments about executive power because such arguments require accepting the principle that it is right for my side to lose in certain circumstances. That's a hard thing for anyone to accept, much less stupid and horrendous people, like Trump and Gingrich.