Is this an original battery for a 2010 VW Golf6?

Look at the lower left-hand corner. It says "VW AG" which indicates this is a VW OEM battery. The "2509" says, I assume that it was made in the 25th week of 2009 which is in line with your 2010 model year.

As to whether this is the original battery in your car, it's difficult to say with certainty but this sure looks like an original TYPE battery for your VW.