I think "kysser" would be "kisses" or "kissing", whereas here you need "kiss", hence "kysse". I could be wrong though.

Without knowing the actual grammatical rule for this in Danish I can confirm that "kysse" is the correct form of the verb in this case.

I think it may have to do with what is the verb in the sentence; which is actually "ser" (sees) so the kissing part becomes something that is being seen and not the active verb? "Kysse" is the base-form of the word, i.e. "At kysse" (to kiss).