Q:

Why could Voldemort's memory from the diary horcrux take physical form? 

Why did the diary Horcrux create a fully fledged Tom Riddle who could walk and talk and stuff when no other Horcrux seemed to do that? 
What was special about the diary that allowed it to do this? 

A:

Why did the memory inside the diary acquire a quasi physical form? 
The Diary was no ordinary diary.  It had the power to draw life force from a reader/writer who got emotionally attached to it and use it to create its own body.  As it happened, Ginny poured her heart out to Voldemort, strengthening him and making herself vulnerable to him.  
So Voldemort used Ginny's life force to create a quasi-body for him.  He would have succeeded in creating a full body, Had Harry not intervened.  
Voldemort did not bestow the power to draw life force to strengthen the Horcrux inside any other of his relics except the diary which is why it stands out. 
What impacts the diary's success in chamber of secrets could have had, JRK had following to say, (quoted from DVK's answer):

Q: In 'Chamber of Secrets', what would have happened if Ginny had died
  and Tom Riddle had escaped the diary? 
A: I can’t answer that fully until all seven books are finished, but it
  would have strengthened the present-day Voldemort considerably.