Can 1900s X-COM fend off the alien invasion?
That's remotely possible. 1900's cool and even inspiring but it's not reality.
X-COM produces and markets video games. It's a business entity seeking to expand its brand. If there were anything of genuine value X-COM could have been bought out by UK or US Department's of Defense.
I admit there's another answer (almost) equally viable. Plagiarism. The X-COM model may have been copied or at least influenced by some government's military plan to defend Earth leaked by programmers in the defense industry. That may explain why it's not set in 2019. If it's based on fact from a real defense plan it can't be too similar to its program of origin. It would be interesting to set the game in modern times.
Lastly, it's a possibility that military powers follow the games progress and evolution for fresh ideas as players come and go. That would mean 1900 is contributing to the defense of the planet.
I think Man shouldn't worry with alien invasions because in the History of Man, that started million years ago after his evolution, according to Man, he didn't see any alien invasion and God knows if Man shouldn't need the help of aliens to stop destroying the nature of his own planet that Man is taking very slowly to the destruction even before alien come in on Earth and invade Man and Earth, so Man should be turned to take measures not to destroy Earth and its nature and all its living beings.