It is significant that the word "Shadow" is capitalized.
There are 224 occurrances of the word "shadow" in the Fellowship of the Ring (including preface and prologues), and Tolkien is very specific with those he capitalizes and those he does not.
I'm (obviously) not going to list all of them, but here is (I hope) a representative sampling:
- In the Land of Mordor where the Shadows lie
- Their own accounts speak of the multiplying of Men in the land, and of a shadow that fell on the forest...
- ...he seemed to grow tall and menacing; his shadow filled the little room.
- ...legends of the dark past, like a shadow in the background of their memories...
- Always after a defeat and a respite, the Shadow takes another shape and grows again.
- ...they became Ringwraiths, shadows under his great Shadow...
- Then Sauron was vanquished and his spirit fled and was hidden for long years, until his shadow took shape again in Mirkwood.
- The black shadow stood close to the point where they had left the path, and it swayed from side to side.
- The shadow of the fear of the Black Riders came suddenly over them again.
- 'Against the Shadow in the East,' said Strider quietly.
- Also we crave the advice of Elrond. For the Shadow grows and draws nearer.
- ...like a great black horseman, a dark shadow under the moon.
- The shadow of Mordor lies on distant lands.
- ...the horses of the Riddermark come from the fields of the North, far from the Shadow...
- Through the opening a shadowy stair could be seen climbing steeply up...
- Great shadows sprang up and fled...
- Away beyond the shadows at the western end of the hall there came cries and horn-calls.
- "The Shadow" is not Moria; Moria is referred to using uncapitalized "shadow".
- "The Shadow" is not Sauron; Sauron is referred to using both capitalized and uncapitalized.
- "The Shadow" is not Mordor; again we have "shadow of Mordor".
The concept being developed here is "Shadow" as an active agency of Evil, which may be personified by Melkor in the First Age (Frodo's words to Sam concerning Orcs - "The Shadow that bred them can only mock, it cannot make real new things of its own. I don't think it gave life to the Orcs, it only ruined them and twisted them." - are also significant here) and by other agents in later ages.
A literal reading is therefore incorrect; what Gandalf is in fact saying to the Balrog is the equivalent of Feanor's "Get thee gone from my gate, thou jail-crow of Mandos!" or "Get thee gone, and take thy due place!". His use of capitalized "Shadow" is him letting the Balrog know that he knows what it is and what it represents; nothing more.