No it doesn't. Here's a benchmark I found showing it running much quicker.

If you really wanted a 2gb 960 then buy this and contact Amazon to give you a £20 refund.

http://www.amazon.co.uk/gp/offer-listing/B00SJ8FZZ0/ref=dp_olp_used?ie=UTF8&condition=used&m=A2OAJ7377F756P

Will this fit in a compact PC? Anyone have the dimensions

Single fan so quite short , 2slots wide should fit most itx cases with 2 slot wide capability.. some cases can only fit single wide cards.. nvidia etc. might bring out a single slot gtx950 soon?

Plenty of recent review showing that 2GB in this GTX 960 and the 2GB version of the R9-380 are near to reaching their limits:

Taken from:
http://www.computerbase.de/2015-12/2gb-4gb-gtx-960-r9-380-vram-test/2/#diagramm-geforce-gtx-960-fps-mordors-shadow-1920-1080
Google Translate.
In other words: there is no automatic 128-bit bus means 2GB is enough. Provided we are not talking 4GB DDR3 vs 2GB GDDR5, more memory is usually useful. Even the 8GB in the R9-390 / R9-390X or the 12GB in the Titan X can make a performance difference in some games.

Just email Amazon support or live chat and ask them- I did it yesterday and they took off 20 quid immediately.

No worries about the 128 bus...4gb are the new minimum.

I don't really know what a 128 bit bus is so you are most probably right with whatever you said above.

What I do know is that this is a 1080p card and no games running at 1080p will use over 2GB and hence 4GB is a waste.