There's definitely the showman/reality TV star aspect to him. I'll come back to that.
as a president he is a republican
The question is, which kind of Republican?
He's definitely not Patrician Republican. He's not West Coast Republican (Reagan/McCain). He lines up pretty well with the former Democrats who flipped when LBJ signed the civil rights legislation, and he taps into that with dog whistles - though his bigotry is different than Southern racism. That group overlaps with Evangelicals, but his personal morals don't make him a good fit with those people - that's a marriage of convenience and as long as he keeps delivering judges like Gorsich, and Pence keeps winking out to them, he'll keep their vote. He's not a Wall Street Republican, though he is Pro-Business Lobby, I'd say mostly because of his business background. So who's left? Reactionary ethnics exemplified by guys like Hannity and Reilly, Scaramucci, Jeanine Pirro, Guiliani, Chris Chritie, etc. etc. If you spend time in the New York area, you know exactly who these people are. That's who he really sits with - they're all more or less from the same place, geographically or at least psychologically - what we call "the Bridge and Tunnel" - areas on outside of Manhattan. Its a certain type of non-Park Avenue New York/New Jersey Republican.
I would further argue, he won over the Rust Belt, the area that actually decided the last election, not with the Republican brand, or his personality, but with populist promises of trade wars and border walls - issues that played to economic insecurities of the post-industrial Mid-West. These were people who voted union up to half a generation ago, and probably also went for Obama in good proportion. Probably would have gone Bernie and definitely would have gone Biden. Aside from all the problems with Clinton, her biggest mistake was aligning herself most visibly with the new Democratic coalition of minorities and women and ignoring the Rust belt that she apparently took for granted.
in terms of policy
Policy wise, he's basically pro-business, spiced with ostentatious disregard for the environment and international coalitions, and half-cocked populist slogans (its remarkable that "Build that Wall" was supposed to be a throwaway line that he didn't even like until the crowds started going crazy for it.)
Since he became a public figure back in the late 70s, he's been a carnival barker/used car salesman, who would do or say anything to move his latest project. Being in real estate, he'd do whatever was needed to sell condos. He was never interested in urban planning. His building are crass opulence.
This willingness to do or say anything to make the sale served him well on reality TV, and then on the campaign trail. That China vid above in a way, shows his method. He finds a theme that gets the crowd wild, and he plays it for everything. He's literally admitted that in interviews. "I just say whatever gets a cheer out of the crowd." He can do this so well because he has no shame.
The Jerusalem embassy thing - you know how popular this has made him among Jews? Mind boggling. He's playing to his orthodox business partners. They're all slapping his back down at Mar a Lago, and calling him saying, "Mazel Tov!" And then he lets some Southern Baptist who thinks the second coming will be advanced by the reestablishment of the Temple in Jerusalem give the prayer at the opening!
People in my town can't even pay rent any more, prices have gone so high since the techy gentrifiers moved in (who mostly see themselves as "liberal" warriors for social justice, in a nice twist of historical irony, as they run the poors out of town)
But, you know, they buy free trade, and make sure the municipality is a sanctuary, so they're doing their part, JD!
Amazon is set to take over parts of the federal government
I dunno, man. If they can make government as efficient as Prime Two Day Delivery, I might hand myself over to Alexa.
Trump's sizable role in things like de-regulation attempts
That's just executive prerogative. The real problem is the Imperial Presidency that we have...
The refusal of the left to deal with concrete issues of our time and instead focus on Trump's (admittedly disgusting) personality is one of the things that enabled him to be president, if people keep doing it, he will be president again, I am pretty sure. It's not hat he's so good at manipulation, it's that his opposition is no non existent that all he has to do is make inane promises to the demographic they are ignoring, throw in some good ol' xenophobia, and he outperforms.
Shoulda been Bernie.
two cents. mind dump.