In SAO, there are no magical spells that players can cast but according to the light novel SAO does have some magical items and aspects. Some of these items are gems that could be used to instantly teleport, heal or recover from poisons. There is also the Divine Stone of Returning Soul that allows a player to bring back a fallen player.
This text and the following quotes are taken from the second volume of the light novel.
The few magic items in this world where had been excluded were all shaped like gems. Blue was for instant teleportation, pink for recovering HP, green for antidotes, and so on. They were all convenient items that produced instant effects, but they were also expensive. So in most cases people used cheaper items such as slow-acting potions after running away from a fight
Certain parts of the game could be considered magical such as the teleportation gates used to move between floors and the alters found in churches. These alters would allow a player to bless their weapons when facing undead opponents. Also if a player was cursed they could use the alter to remove it.
It was the unmistakable mark of a church, of which at least one exists in every town. And through the altar inside, tasks such as removing the attack unique to monsters, «Curse», and the blessing of weapons to go up against undead monsters with, were possible. In SAO, where magic-based components barely exist, it could be considered a most mysterious place.
As for Elucidator it is not a magic sword but a demon sword as stated in the light novel. While both the english sub and dub refer to it as a magic sword. As said in the comments I also believe it is an error in translation. So there are no magical weapons in SAO but they do seem to have other forms of magic.
One is «Player made», which meant weapons made by us blacksmiths. The other included weapons that one gained from adventuring as «Monster drops». Needless to say, blacksmiths don't like drop weapons all that much. I couldn't even begin to count all the names like 'Unnamed' or 'No brand' that were given to them. But this sword seemed to be a very rare item amongst monster drops. If you compared the average quality of player-made weapons and monster drops, the former was better. But once in a while, «Demon Swords» such as this one appeared— that was what I heard.