Is Moving tempdb Files to Different Disk Drive Beneficial if All LUNs Are from Same RAID Pool?

A few notes here:

1. You definetely have to separate the files logically using different partitions (I recommend separate partitions for: system, data files (mdf/ndf), transaction log files (ldf) and tempdb files (mdf/ndf). Where you put the tempdb transaction log file is up to you (tempdb drive or log drive), I'd go with log drive.
2. Backup files should not be on the located same device and especially the same VM (I recommend a different SAN/NAS).
3. Placing your data, log and tempdb files on different drives is mostly a way of improving performance. Transaction log is heavily written and is probably the slowest component of SQL Server. The second bottleneck is by design the tempdb database. If these 2 components are placed on different drives (especially if they reside on SSD/RAID10 disks), the performance will be definitely better.
4. You can keep the transaction log and tempdb on the same array as the user database files if you aren’t experiencing performance problems (at least not yet). I would look at the sys.dm_io_virtual_file_stats DMV to verify if there really is a problem with IO performance.
5. If you want to move these files to a different disk in a virtual environment you can create a separate virtual disk for every partition you want to move and assign these disks to different LUNs in the array.

First verify if what you're seeing is the same as what SQL Server can see, by running this:

USE tempdb;
EXEC sp_helpfile;

If all 3 of your files are here, you somehow created them there by accident.

TempDB is a 'special' system DB that gets re-generated every time you start the SQL Server service.

Setup TempDB the way you want it, restart the server so TempDB recreates itself and run the above query again, to see if the new settings stuck.

If you want to still add a file somewhere manually you can do this:

ALTER DATABASE tempdb ADD FILE (
    NAME = N'LogicalNameHere'
    ,FILENAME = N'D:\Whatever\tempDB2orWhatever.ndf'
    ,SIZE = xMB
    ,FILEGROWTH = xMB
    );

If you want to keep all of your TempDB files but just move them around, get the info from sp_helpdb and modify to include your paths/files/names as found here:

USE [master];
GO

ALTER DATABASE tempdb MODIFY FILE (name = tempdev, filename = 'E:\Sqldata\tempdb.mdf');
ALTER DATABASE tempdb MODIFY FILE (name = templog, filename = 'E:\Sqldata\templog.ldf');

Note you should usually have multiple TempDB data files. If you don't, you are risking logical file contention, which is not pretty.

Check out Brent's blog for more info on SGAM and PFS contention.