The most likely reason I can think of is that there are in fact three versions of the DeltaWing. The first, designed by Ben Bowlby for Garage 56 at Le Mans, was built by All American Racers (AAR), campaigned by Highcroft Racing, and backed by Nissan and Nismo. The car featured a 2.0 straight-4 with a Nissan DIG-T direct injection system. Nissan provided most of the funding for the project and was thus entered as the "Nissan DeltaWing", and the car competed in 2 events in 2012 - Le Mans and Petit Le Mans. The car was specifically designed to race at a pace similar to LMP2 class cars because the ACO did not want an unclassified car which did not meet their ruleset to be able to compete for the overall race victory.
In 2013, Don Panoz bought DeltaWing Racing Cars and their intellectual properties. This effectively took the car out of the hands of AAR, Highcroft, and Bowlby himself, and severed the company's ties with Nissan. Panoz planned to use a turbocharged Mazda 1.6 straight-4, tweaked by his own in-house Elan Motorsports arm, to produce more power and move the car into the LMP1 category. The car was redesignated the DeltaWing "LM12." This car ran the majority of the 2013 ALMS season as an LMP1 until it was replaced by the DeltaWing Coupe, "DWC13".
The car featured in GT6 is the Nissan DeltaWing, and likely part of a licensing agreement between PD and Nissan, with Bowlby also approving of the agreement since he now works for Nissan on the ZEOD RC. However, Panoz does in fact own the physical design of the DeltaWing, so Nissan's permission is likely not enough to include the car in the game. In short, because the original design changed ownership, Nissan no longer has control over a car they marketed.
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As for the "gimmick" of the DeltaWing design, the car is meant to address several issues in the modern racing world, specifically Le Mans endurance racing. First, it is extremely light compared to the 900kg cars in LMP, not only because of its narrow front track but also because of its construction. Since it is so light, a smaller, less powerful engine is all that is needed to equal the lap times of an LMP car. The original Nissan powerplant was a mere 200hp, yet equal on pace with the majority of the LMP2 field. LMP2 pole qualifying time at Le Mans in 2012 - 3:38.1, DeltaWing qualifying time at Le Mans - 3:42.6, on its first ever competitive outing, slowest LMP2 on the grid - 3:48.0.
Because the engine is not only low in horsepower, but also not a stressed member of the chassis, the engine possibilities are not only endless, but relatively cheap, since a simple production motor can handle the job. In fact the Nissan unit was in actuality an older WTCC unit adapted with direct injection. And since such a lower power engine saves on fuel economy, you need to make less pit stops. Do you think Audi switched to diesels because of a gimmick, or because it gives them an advantage in endurance racing since they use less fuel?
Further, because of the light weight, and even with its unique tire design, the DeltaWing was able to quadruple stint its tires, saving further cost for teams and improving its race performance by lowering its amount of time stopped for tire changes. Now, bear in mind that at Le Mans, Highcroft and the DeltaWing team specifically did not attempt to save time in the pits through this method, in fact the car had to be wheeled into the garage every time they wanted to change tires because an appropriate jacking system was not in use yet. But still, the point is there, the DeltaWing uses less tires and less fuel and thus requires less pit stops. That is an advantage, not a gimmick.
So in the end you have a car that is able to match the cars of today with a radical rethink of race car design, has better performance potential thanks to its design and weight savings, and is likely to buy for the majority of racing teams. Add to this the ZEOD RC, which is attempting to complete a lap of Le Mans under full electric power. Light weight is key to making electric vehicles work, so the DeltaWing design is perfect for the project. Nissan isn't just trying a marketing gimmick, the ZEOD RC is part of their development for a 2015/16 LMP1 for the company.
As for the struggles of the DeltaWing in 2013 and its lack of pace and/or endurance, the answer to that is simple - Panoz doesn't have the man power or money to make the car work properly, has lesser drivers involved, is attempting to build his own bespoke engine unit for the car without much success, and concetrating much of his time and money on the development of a coupe version. The 2013 car is effectively worth ignoring.