“Ah, now, I’m glad you asked me that. It was one of my more brilliant ideas, and between you and me, that’s saying something. You see, only one who wanted to find the Stone — find it, but not use it — would be able to get it, otherwise they’d just see themselves making gold or drinking Elixir of Life. My brain surprises even me sometimes...
-Harry Potter and the Sorcerer's Stone.” -Chapter 17-The Man With Two Faces.
Dumbledore quotes this to say a person who wishes to use the elixir of life can't bring the stone out of mirror. He also says that the person would just see himself making gold or drinking the Elixir of Life.
But Quirrell doesn't understand how to get the stone out of mirror, it implies that he sees nothing than just a reflection of himself in the mirror.
“What does this mirror do? How does it work? Help me, Master!”
-Harry Potter and the Sorcerer's Stone.” -Chapter 17-The Man With Two Faces.
Now the main part is, Quirrell did not intend to use the stone for himself. He wanted to present it to his master, which is for a valid reason, he can take the stone out of mirror as per the reason said by Dumbledore.
Why was he unable to see the stone in Mirror?