its a race built seqential gearbox, its very similar to an F1 gearbox, but no paddle shifters. Instead its just a bar he pushes forward for a downshift, and pulls back for an upshift. With a sequential gearbox the driver can only go gear for gear, so 1->2->3->4 or 4 ->3->2 etc, which is faster than a traditional manual.
if anyone was wondering, http://www.racecarsdirect.com/ has sold more then a few btcc cars (including the one in the vids iirc). they even have nigel mansells '98 for sale.