Not enough server storage is available to process this command - RESTORE DATABASE is terminating abnormally
The error message is misleading you, it's not talking about disk storage on the machine where you are restoring.

The windows error message states:


  1130(Not enough server storage is available to process this command.)


When you check that error message you will notice that it's not an error during the restore operation but rather during the file copy operation over the network as documented here


  The two causes of this problem are related. The more frequent cause is listed first:
  More files are open than the memory cache manager can handle. As a result, the cache manager has exhausted the available paged pool memory.
  The backup program has tried to back up a file whose size is larger than the backup API can access on that version of the operating system. This has the same result (that is, the paged pool is exhausted).
  Note This second issue is more likely to occur on a Microsoft
  Windows NT 4.0-based computer.
  
  The resolution for each problem differs depending on whether you
  experience the problem in Windows Server 2003, in Microsoft Windows
  2000, or in Windows NT 4.0.


Or here


  When you access shared items on a Windows NT server from a Windows NT
  client, you may receive the following error message:   Not enough
  server storage is available to process this command.


So as you say, you likely have enough storage to restore the database but you are running into issues retrieving the file over the network. 
In any case you need to be looking at some SMB issue

Had you been running into disk space problems during the restore the error message would have been: 


  112(There is not enough space on the disk.)


As @Nic correctly pointed out in the comments you should probably try to copy the backup file over using an unbuffered file copy (use ESEUTIL or XCOPY) and restore from there to either solve or at least isolate the issue.

If you still run into issues copying over the file that way I'm not sure that still fits the scope of dba.se.