If we're interpreting the scene that Hamlet wrote about in his answer (I haven't read the books recently enough to recall whether Regulus' Quidditch position is mentioned elsewhere), I have another, perhaps simpler explanation.
I think that Regulus' position is mentioned, specifically noticed by Harry, to create some form of kinship or connection between Harry and Regulus.
The friends start with the initials R.A.B., not sure who or what they signify, and eventually find out that those are Regulus' initials. Then they're not sure whether he's a "good guy" or not (most of the Black family members are proudly on Voldemort's side, after all); when they enter his room and find the green and silver, that would initially make them believe that Regulus was working against them.
However, once they discover that Regulus is a Seeker, Harry can begin to allow himself to feel something toward Regulus as a friend or ally. This makes Kreacher's story, establishing Regulus as an agent against Voldemort and his Horcruxes, somewhat more believable to the friends (and the readers).
To set the scene: the friends discover the meaning of the letters R.A.B., and then cautiously set out to find what they can from Regulus' room. They can assume that he was not their friend because of his lineage (I don't recall whether they knew at this point that he was once a Death Eater), but then Harry finds something interesting:
Harry, meanwhile, had noticed another photograph: a Hogwarts Quidditch
team was smiling and waving out of the frame. He moved closer and saw
the snakes emblazoned on their chests: Slytherins. Regulus was
instantly recognizable as the boy sitting in the middle of the front
row: He had the same dark hair and slightly haughty look of his
brother, though he was smaller, slighter, and rather less handsome
than Sirius had been.
So he's a Slytherin, which initially supports the possibility that he's not a friend of Harry's, but he can smile and wave in a picture*. He also looks like Sirius. And then Harry discovers something that is more important to him:
"He played Seeker," said Harry.
"What?" said Hermione vaguely; she was still immersed in Voldemort's
"He's sitting in the middle of the front row, that's where the Seeker
... Never mind," said Harry, realizing that nobody was listening.
If many people can be friends with someone simply because they attended a school that they did, I can understand that Harry can relate to and start to feel good feelings toward someone who was also a Hogwarts Seeker. After this preparation, they are now ready to hear Kreacher's testimony, now ready to accept Regulus as the good guy that he was.
* I don't have the books on hand at the moment, so I can't really support this very well, but I'm pretty sure that no "bad guy" in Harry Potter was ever shown "smiling and waving" in a photograph. Sirius Black, for instance, before the reveal that he was set up and was actually one of the best "good guys" in the books, was known only by his crazed mug shot. I can't really say without evidence, but I wouldn't be surprised if pictures are consistently used in the books by Rowling as a device to illustrate a person's "goodness."