When someone thanks you for something, you can say "My pleasure". Maybe the person who wrote this in the chat made a mistake and said "your" instead of "my".

From my perspective, A complimented B. But for A to say "My pleasure" would be more correct instead of "Your pleasure". "My pleasure" is short for "It was my pleasure [to do such and such]", as a way of saying "It-was-no- problem-on-my-part-to-do-what-you're-thanking-me-for" instead of "You're welcome". I think it is usually used in a formally polite or charismatic way by a person responding to an acknowledgment that they have cordially done a favour which takes fair bit of time, without hassle, for another person. In your conversation, I think it was used because their compliment was a personal one and they wanted to express charisma, so they used a more elegant phrase like "My pleasure" which carries a little more weight than "You're welcome".