MissScarlett: I think I can provide clarity.
In <Lasker & His Contemporaries>, Thinker's Press (1997), No.5, pp.23-32, John Hilbert's article, <The Walbrodt-Delmar Match, New York 1893> gives the score of all eleven match games. However, his first two games are actually non-match games played the month before, as referenced by <heuristic above>. Whoever uploaded the games to <cg> was apparently misled by this misattribution. Hilbert also incorrectly gave the first two match dates as April 23rd and 24th, whereas the <Sun> article mentioned by <mifralu> reveals they were both played on the 23rd.
The source of Hilbert's error was his reliance on what he calls <Delmar's Scrapbook> (presumably Delmar's personal record), <which includes newspaper accounts of the match, most probably from the New York Sun>.
This is the key point because it's clear that some, if not all, of these newspaper accounts must have been cut and pasted into the <scrapbook> without inclusion or record of the paper and date (although Hilbert correctly infers the Sun was the actual source of most, if not all).
Hilbert quotes excerpts from two such notices for the first two games, and one can seen how he could have been confused:
<Walbrodt began a series of games with Delmar [...] at the Manhattan Chess Club yesterday. [...] [Delmar] had to give up the fight after forty-six moves.>
<[W]as played at the Manhattan Chess Club yesterday in the presence of a large gathering of members of the club. [...] Walbrodt struggled on to the forty-sixth move. It may be worthy of mention, that Delmar lost the first game in exactly the same number of moves.>
<heuristic> is correct that these games were played on the 16th and 17th of March, as the (New York) Sun articles quoted are from the 17th and 18th, respectively, but I don't think calling them casual or off-hand games does them justice, and that <exhibiition game> is preferable.
I assume all the other match game scores, with their corresponding <Sun> notices, are correctly attributed by Hilbert, but I haven't checked them as yet.
Suffice to say, some corrective work to my match collection is required. Hilbert is not, to my knowledge, a <cg.com> member, so I suggest any personal attacks are addressed in his direction.