Preliminary arrangements appeared in the <British Chess Magazine>, August 1889, p.318. Of course, they also appeared in the German tournament book cited below, but I'm not going to inflict that on you or myself.
Amsterdam 26 Aug - 1 Sept
<"An International Chess Congress will be held at the Cafe Red Lion, Vygendam, Amsterdam, beginning on August 25th. There will be three classes, the first to consist only of acknowledged foreign masters, and some of the strongest Dutch players. Hours of play, 12 to 4 pm., and 6-30 to 10-30, each competitor to play one game with every other and two games each day, except on three evenings of the week, when unfinished games will be played out. If the entries do not exceed seven, it will be a two-round tourney. Time limit, 18 moves per hour. The committee will decide in which class each competitor will play.">
1 2 3 4 5 6 7 8 9
1 Burn * = = 1 1 1 1 1 1 7.0
2 Lasker = * = 0 1 1 1 1 1 6.0
3 Mason = = * = = = 1 1 1 5.5
4 Van Vliet 0 1 = * = 1 = = 1 5.0
5 Gunsberg 0 0 = = * = = 1 1 4.0
6 Bauer 0 0 = 0 = * 1 = 1 3.5
7 Loman 0 0 0 = = 0 * 1 1 3.0
8 Van Foreest 0 0 0 = 0 = 0 * + 2.0
9 Leather 0 0 0 0 0 0 0 - * 0.0
These players impressed the Committee sufficiently to gain admittance to the top group:
Johann Hermann Bauer;
Arnold van Foreest;
Robinson Kay Leather;
Rudolf Johannes Loman;
Louis van Vliet.
Of these, Burn, Gunsberg, and Mason were already veteran Masters. Bauer and Lasker were less experienced interationally, having qualified as Masters by winning <Hauptturniers> at the German National Congress. Lasker, indeed, had done so only a month earlier.
Van Foreest was the current Dutch champion. Loman and Van Vliet were native Dutch players, though they resided in London at the time. Finally, there's Mr. Leather, a professor at Liverpool University. There is a report that Blackburne had entered and was expected to play, so Leather might have been promoted from a lower section to produce an even number of players. When Blackburne never showed up, Leather was allowed to remain in the Master section though he proved to be outclassed.
Lasker started well, winning his famous double-bishop sacrifice game against Bauer in round 1 and sprinting to a 3-0. A loss to Van Vliet in round 4 dropped him into a three-way tie for first with Gunsberg and Mason, while Burn (who had scored a draw and a bye in the first two rounds) kept chugging along, making up ground.
Lasker got his bye in round 7, and Burn took the lead with his fifth straight win. The Englishman made it six straight in round 8, clinching a tie for first as Lasker drew. The younger man did have a chance to catch up in the last round when he had White against Burn, but settled for second place with a quick draw.
Two games are missing. Mason and Bauer did not submit a score from their round two game, and Leather, having lost every game, departed before his last round game with Van Foreest.
Fuller details can be found in the original tournament collection.
British Chess Magazine, August 1889, p.318:
Der Internationale Schachkongress zu Amsterdam im August 1889 / bearbeitet von Jur. Das. D van Foreest und Cand.-Jur. L. D. Tresling. Utrecht : J.E. Beijers, 1891.
Yellowine's News, September 29, 1889.
Original collection: Game Collection: Amsterdam 1889, by User: Phony Benoni