I believe Regulus didn't know that the Dark Lord had made more than one Horcrux.
Think about it.
It is unprecedented to have more than one Horcruxes. The Dark Lord doesn't talk about them even to the most trusted servants, and had hidden the other Horcruxes well. Regulus had died long ago: certainly before the Dark Lord had risen again (as Sirius has already owned the family house at the end of Prisoner), and very likely before the Dark Lord had fallen. He didn't see the Dark Lord rise again and hear the Dark Lord's statement saying “I, who have gone further than anybody along the path that leads to immortality”, which is the statement that has given Dumbledore a clue about multiple Horcruxes. Regulus likely hadn't even lived when the killing curse has rebound on Harry. He likely doesn't know about what's happened in the Chamber of Secret. He certainly hasn't seen Nagini as a Horcrux, as that Horcrux was created only the summer after Harry's third year. He certainly doesn't know about Riddle's conversation with Slughorn. In short, Regulus didn't know about enough clues to guess that the Dark Lord had made more than one Horcrux.
Consider also the note Regulus wrote in the fake locket. (Half-Blood Prince chapter 28, quoting just parts of it here.)
… it was I who discovered your secret. I have stolen the real Horcrux and intend to destroy it as soon as I can. I face death in the hope that when you meet your match, you will be mortal once more.
Regulus clearly knows what a Horcrux is and that the locket is a Horcrux. But “your secret” could refer to just one Horcrux, as the Dark Lord has certainly kept it secret that he had even one Horcrux. The rest of the note is also consistent with believing that there's only a single Horcrux.