Why is it necessary to get Slughorn's memory?

You're quite right: Dumbledore already knew that Voldemort had created Horcruxes. Your confusion may stem from the fact that the word "Horcrux" isn't mentioned in the altered memory, whereas it is in the book. But there's no question that he knew about them.

What Dumbledore didn't know - and what he suspected Slughorn knew - was how many Horcruxes Voldemort had made. Two had been destroyed by that point - Tom Riddle's diary and Marvolo Gaunt's ring - but Dumbledore didn't know how many others were still out there, and the sooner he found out, the sooner he and/or Harry could set about tracking them down and destroying them.

In the original, unaltered memory, Tom Riddle raises the possibility of splitting his soul into seven pieces - one inside himself, and six inside Horcruxes. This is indeed the exact number of Horcruxes he made (discounting Harry, who he made accidentally and is arguably not a Horcrux anyway).

The movie diverges quite significantly from the book in this area. The movie script of the first (edited) memory contains this dialog:

Tom Riddle: I was in the library the other night. In the restricted section. And I picked something rather odd about this rare magic. I thought perhaps, you could illuminate me. It's called, as I understand it, Hor...

Horace Slughorn: I beg your pardon? I don't know anything about such things and if I did, I wouldn't tell you. Now get out of here at once and don't let me ever catch you mentioning them again!

So its clear from the script that in the tampered memory that Dumbledore originally has, Riddle doesn't mention Horcruxes explicitly (though the 'Hor...' surely would give Dumbledore a clue).

So I believe the script writers were trying to set up the situation where Harry is used to discover both the name and the magic used and reveal the extent that it was used.

I mentioned all that because I think it makes your question about the ring relevant. If Dumbledore discovered and destroyed a Horcrux already, why does he need the memory?

It is possible that Dumbledore only knows for sure that the ring contained a powerful curse. He may have suspected that it was a Horcrux, but needed the memory to confirm this. The real memory may also contain important additional information that they could use to defeat Voldemort, so he had additional good reasons to try to obtain it from Slughorn.