For what?
Did this memory provide anything that wasn't explained or was difficult to explain or something else?
The doll itself with the earrings already tell us that there is a connection to Tanjiro, then there is Tanjiro's birthmark, which gets bigger when he does this Sun(? can't remember)-breathing of his. The hair - even the doll has the "mark" in some way. Then there was the Demon in episode 1 this season who lived for hundreds of years and has this same mark as well (+ another one on the lower left of his face from who knows where/how/what it means - probably a different guy or generation btw, because it's a different sword + a different voice actor...)
So obviously, there are connections established already and the memory didn't give us any more to work on imho.
I mean - okay, if we assume the demon and the swordsman (for reasons mentioned above) are not the same, I guess we got some new information out of it that would be "hard" to explain. But at the same time it's not like the information was necessary for something that wasn't already shown/told otherwise.