The last time the World Chess Championship was held in New York City, titleholder Garry Kasparov met challenger Viswanathan Anand on the 107th floor of the south tower of the World Trade Center. They played their first game on Sept. 11, 1995.

That tower is now gone, a new one stands nearby, and the grandest board in chess is again set in lower Manhattan. This year, the venue is the new Fulton Market Building in the South Street Seaport, an area of the city that was ravaged by Hurricane Sandy in 2012. It was rebuilt and has been thriving in recent years.

The players are different, too. Magnus Carlsen of Norway, ranked No. 1 in the world, is defending his title against Russian challenger Sergey Karjakin, ranked No. 9. The first weekend of their best-of-12 match is in the books, and after two games — and two draws — the score is level at 1-1.

This year’s chess venue is sparse and sleek, heavy on concrete and hypermodern black-and-white branding. Large flat-screen televisions dot the open floor, providing live views of the tense and slowly unfolding games. The sellout crowd mills around, stealing meaningful-looking glances at the game on TV, listening to live commentary on headphones, eating sandwiches and playing their own games of speed chess in the cafe’s Eames-style dining chairs.

The two grandmasters play alone in a separate room, accompanied only by two stoic match arbiters. On the inside, the room resembles the bridge of a sci-fi spaceship. To the spectators on the outside, though, it evokes a reptile house in a zoo. You enter the dark, hot and humid viewing gallery through thick black curtains. You’re hushed as you enter and reminded to silence your phone. The lights inside are dimmed, and an eerie purple light glows from behind the thick glass of the one-way mirror. You can see Carlsen and Karjakin, leaning in close to each other over the board in deep thought. They can’t see you.

In Game 1, Carlsen, playing with the white pieces, chose an unusual opening called the Trompowsky Attack. The joke around the Fulton Market Building on Friday was that he played it as a homophonic nod to the new president-elect. There was truth to the joke. Asked after the game whether his choice had anything to do with Donald Trump, Carlsen replied: “A little bit.”

“I’m a big fan of Donald Trump,” Carlsen told Norway’s TV2 in March (in Norwegian). “Trump is incredibly good at finding opponents’ weaknesses. He speaks only about that the other candidates are stupid or smelly. There should be more of this in chess, too.” Carlsen then offered a Trumpism of his own: “Karjakin is incredibly boring!” Karjakin, for his political part, is an avowed supporter of Vladimir Putin.

By the end of that first game, each side had pushed its wooden army as far as it’d go — two phalanxes scrumming at the center of the board. No further blood was drawn, however, and the players agreed to a draw after the 42nd move and just under four hours of play. (Draws are quite common in championship chess.)

On Saturday, as thousands of protesters, dissatisfied with the results of the presidential election, were marching from Union Square to Trump Tower, just a few miles north, the two grandmasters sat down in the spaceship to play again. Game 2, with Karjakin handling the white pieces, began with the all-too-familiar Ruy Lopez opening, a staple of chess for 500 years. The rest of the game was an equally uncreative and plodding affair. One prominent grandmaster on Twitter called certain passages “flaccid.” After just under three hours, and not much else to speak of, they arrived at a second draw. (The computer chess engine Stockfish was in full agreement, seeing both games as nothing but deadlocked.)

The actor and chess fan Woody Harrelson was on hand for Game 1. The star of “True Detective” brought to my mind that show’s oft-quoted line, bastardized from Nietzsche: “Time is a flat circle.” In chess, and at this championship, what’s old is new again, and moves and characters are strangely familiar. Donald Trump made the ceremonial first move at a qualifying event for that 1995 New York championship, at Trump Tower. And Rudy Giuliani, then the mayor and now rumored to be high on the list to be Trump’s attorney general, made the ceremonial first move in those finals. (Giuliani was late — and made the wrong move.)

Carlsen remains the heavy favorite, although his chances according to my Elo-based simulations have dipped from 88 percent at the start to 84 percent now, as Karjakin has held serve. The players seemed to sense that the large crowds were getting a bit restless. “I ask you for your understanding that this is a long match,” Carlsen said at Saturday’s postgame press conference. “Not every game will be a firework.”

Game 3 begins Monday afternoon. I’ll be covering the rest of the match here and on Twitter.