How is McEliece chosen plaintext secure?
Does this attack work?


Yes, it works.
However, "textbook" McEliece was never claimed to be IND-CPA.
In fact, it was already published in 2008 by Nojima et. al. in "Semantic Security for the McEliece Cryptosystem without Random Oracles" (PDF).

They also propose a mitigation in the paper, which is to simply front-pad the message with sufficiently many random bits and later simply ignore those bits at decryption.