That could be if it had been: La virino kisas vin'.
(Note the final apostrophe.)
Though this replacing of -o (for a noun) or -a (for "la") with an apostrophe is usually only done in poetry or songs.
But the grammar would be wrong, since you would need the accusative here, vinon, and you can't abbreviate that to vin'.
For example, the second verse of the Esperanto hymn La Espero starts Sub la sankta signo de l' espero.
I've seen it most commonly in that combination (i.e. de l'). I'm not entirely sure of the situations where this abbreviation of la is possible.
Note that, unlike French but like e.g. Greek, la remains a separate word even when abbreviated; it is not written together with the following word (de l' espero and not del espero or de l'espero).
why vin and not vi?
Because "you" is the direct object here -- the person directly affected by the action of kissing.
So much confusion in language-learning arises because English "you" fulfils four functions (singular, subject; singular, object; plural, subject; plural, object).
Perhaps it can help if you replace "you" by some other pronoun such as "he" or "she".
"The woman kisses he."
Doesn't work, does it? You need an object pronoun: "The woman kisses him."
And for the same reason, you need La virina kisas vin. here, with object pronoun vin, not subject pronoun vi.
I don't know why I sometimes misheard ni to mi. These pronouns in esperanto all sound somehow the same ending -i. Ni and mi almost sound so simmilar to me that I may have misheard it.
Also Ni and ne also made me misheard also since in the language I use to speak, i and e are actually the same except the loanwords we use from Spanish and English.