Okay, every other commenter here is talking about how baseball is the national pastime. And, I think you understand that.
I'll rephrase the question a bit here: How could any idiot white male raised in the US in the last 120 years possibly not know about baseball?
What I think was happening was that the US GIs would ask the infiltrating German about current baseball. Not Ty Cobb stuff, but Ted Williams stuff.
Also, for the non-baseball fans here, you have to remember that there were only 16 (28) teams back then [0], essentially no trading of players, and no interleague play. So for your team, you really had to know the core 8 players and a few pitchers. Adding in the other 7 teams gets you to ~80 or so (maximum) and they would reappear on the exact same teams year after year. And there really wasn't any other sports worth mentioning in 1943 [1]. Cognitively, it's a lot less than today.
Also, the Germans wouldn't have access to the information about the 'current-ish' state of the game. It was mostly in newspapers back then, and with the war, getting information from the sports pages out of St. Louis wasn't happening.
Same as it ever was, sports is the lingua franca of the US.
[0] 8 in MLB-NL and 8 in MLB-AL, 6 in NL-NL and 6 in NL-AL (yes, the Negro leagues are the major league, but black GIs weren't on the front lines where Germans would be infiltrating (yes, it's more complicated than this simple comment))
[1] The NFL was pretty nascent still.