No, this usage of "mein" is not correct. It has to be "meine" since the grammatical gender of "(die) Wassermelone" is female in German. You might possibly think it could be "meine" because "(die) Katze", which is female in German, is expressing this sentence, but the gender of the speaker doesn't matter at all.
So the grammatically correct version of the meme is
Das ist meine Wassermelone. Meine.
From what I can tell from that answer, mein is for singular male, and
meine is for everything else.
"Mein" is also used for singular neuter, as in
Das ist mein Haus.
If it is accurate how so; since there's only one cat in the image?
Even if there were multiple cats in the image, the inflection of the possessive pronoun would still solely depend on the gender of "Wassermelone" and thus the sentence would have to read
Das ist unsere Wassermelone. Unsere.