I have never heard this expression before, but find it very interesting. Its also interesting that the two baseball related origin stories proffered so far are exact opposites. And I find it interesting that the non-baseball usage seems to be remarkably parallel in usage and meaning to the baseball usage.
In fact, the usages are so parallel that I suspect, but am of course just speculating, that the base ball usage was borrowed from the broader, more general term. But I wouldn’t be surprised if there was a specific base ball game involving the actual Chicago base ball team that led to the general term being extended to base ball. So, in a sense, it may still be true that the baseball application of the phrase emerged from a specific base ball game. Assuming this utterly unsupported speculation is true, this still leaves the question of whether the game that led to the term being applied to base ball was one where Chicago shut somebody else out or got shut out.
I’m probably reading either too much or too little into this, but based on the way the word is used in the above examples, it would make more sense to me if the “true” origin story, at least baseball wise, was that the phrase was coined when Chicago shut somebody else out, rather than it coming from Chicago getting shut out. The three usages I see are: “To Chicago” means to shut somebody else out (and beat them handily). If I am shut out, I “got Chicagoed”. If I shut somebody else out, I “Chicagoed” them.
If the term came from Chicago getting shut out, I would expect the gerund “to Chicago” to mean something like “to choke” (i.e, to score no runs). Since “to Chicago” is to beat another team handily, the sense seems to be that Chicago is the shutter outer, not the one who got shut out.
The fact that “getting Chicagoed’ means “getting shut out” doesn’t really cut one way or the other: it seems to me that it is never a good thing in any sports metaphor to be the person or team who is on the receiving end of an active verb. Even with the example of “choking”, an active verb which is commonly used when commenting on sports and which has a very negative connotation, you still wouldn’t want it said that your team “got choked” (I’m not even sure what that would mean, metaphorically speaking, but I’m sure that it would be bad). Similarly, the fact that “Chicagoing” another team means you are beating them doesn’t really shed light on whether the origin is Chicago winning or Chicago losing, since, either way, you want your team to be Chicagoing somebody else, not to be the one that got Chicagoed. In fact, even if I had absolutely no idea what the term meant, if somebody asked me if I’d prefer it if my team Chicagoed somebody else or got Chicagoed, I would be pretty comfortable guessing that I would rather that we Chicagoed the other team. But the fact that the “gerund” form of the word, to Chicago, means to shut somebody else out, seems to me to support the story that it comes from Chicago shuttting somebody else out.
Although this still doesn’t really resolve anything, I think the non-base ball uses that were quoted also support the idea that in this expression, Chicago is the metaphorical trouncer, not the trounced. There is some convoluted logic in this, but I think it follows.
In one of the non-baseball examples, a New York newspaper headline triumphantly cries, “Chicago Chicagoed!” and proceeds to tell a story of it (New York) outperforming Chicago. In this example, the reference to “Chicago” is literal, but the reference to it being “Chicagoed” is metaphorical. The article seems to be taking great delight in the fact that, at least according to this writer, New York outdid Chicago at the very thing Chicago is known for being great at. The writer also seems to me to be punning on the literal and metaphorical senses of Chicago - of all the cities that New York might aspire to “Chicago” (i.e., to out do), what greater victory would there be than to Chicago the actual Chicago? If the origin of the phrase came from the actual Chicago floundering badly at something (whatever that might be), then the newspaper’s crowing of, “Chicago Chicagoed!”, would be a lot less amusing. Indeed, there would be nothing newsworthy about Chicago being Chicagoed if Chicago is known for being Chicagoed.
Or maybe the baseball usage of the term came from Chicago being shut out, but it was originally used ironically. In other words, Chicago gets clobbered 9 to zero, and a Chicago sports fan sadly sighs, “oh yeah, we really ‘Chicagoed’ those guys, didn’t we. I hope we ‘Chicago’ Baltimore next week.” The speaker in this example would be turning the non-baseball sense of the word on its head: Chicago has gone from the metaphorical trouncer to the metaphorically (and literally) trounced. The ironic application of the term is forgotten over time (and, still later, the term is almost completely forgotten).