Were runes magic letters, or just the Vikings' alphabet?

Both, depending on when you look. The word rune comes from a Proto-Germanic form meaning 'secret, mystery', and in the early centuries runes really were a secret: during the Migration Period the Elder Futhark was known only to a literate elite, with only some 350 surviving inscriptions. The earliest secure runic inscriptions date from at latest AD 150, and most early ones just name a craftsman or an owner. Because of that, it is possible that early runes served as magical signs for charms rather than as a simple writing system, though there is no direct evidence they were ever used for divination.

By the Viking Age the picture changes. The Younger Futhark was a reduced alphabet of only 16 characters, and literacy in it became widespread, shown by some 3,000 runestones, sometimes inscribed with almost casual notes. A runestone is typically a raised stone with a runic inscription, usually a memorial to a dead man, and most date from the late Viking Age.

These stones talk to us directly. One at Lingsberg remembers a man who had taken two payments in England. The Ingvar Runestones remember an expedition to the Muslim world that ended in tragedy, since none of the more than 25 stones raised in its memory tells of any survivor.

And the stones tracked politics: King Harald Bluetooth, newly baptised, commanded a runestone to mark a new order, and others copied him. In Uppland about 70% of the stone inscriptions are explicitly Christian.