No it doesn't. That's physically impossible. Read what you quoted -- it never says that it's going to do it
only for the file in question.
If you don't know why it's not possible, here's a simplified version of it: hardware protocols (s.a. SCSI) must have fixed size messages to fit them through the pipeline. I.e. you cannot have a message larger than the memory segment used for communication with the device, because that will cause fragmentation and will lead to a possibility of message being corrupted (the "tail" being lost or arriving out of order).
On the other hand, to "flush" a file to persistent storage you'd have to specify all blocks associated with the file that need to be written. If you try to do this, it will create a message of arbitrary size, possibly larger than the memory you can store it in. So, the only way to "flush" all blocks associated with a file is to "flush" everything on a particular disk / disks used by the filesystem. And this is what happens in reality when you do any of the sync family commands. The difference is only in what portion of the not-yet synced data the OS will send to the disk before requesting a sync, but the sync itself is for the entire disk, there aren't any other syncs.