This conversation is making my elephant very confused... Based on interpreting my reactions, did I just get negged?

Analyzing...

...Not in the pure sense of "negative compliment". Because, well, I seem to have neglected the 'compliment' part. Let's see... You have beautiful eyelashes... Are they real?

Nevertheless, the style of interaction could be used in a similar social role to the neg - that is, demonstrating playfulness, arrogance and a willingness to assert themselves higher in status (at least for the purpose of that one social transaction.)

To a certain extent there is the reverse of a neg. Surface level cavalier contradiction which nevertheless serves to overall lend support to your position. In particular the replies in the grandparent could be replaced with "Not to me.", "Oh, no, I didn't want to imply that you were being objectionable and using that strategy is OK." and "You are totally right." respectively without changing the object level meaning drastically. Yet that would have conveyed an entirely invalid connotations of supplication and wishy-washy backtracking. Complimentary-contradiction and then flippant elaboration avoids that frame.

In summary: No, but with that style of interaction adding negs would be overkill!