The fighter jet in question is an Aero L-39 Albatros, made from 1971-1996 and used by the Soviet, Czechoslovakian, Libyan, and Syrian Air Forces. Syria still has 61 units in service, while Libya has 10. In both cases, the L-39s are used for training until the pilots are good enough to graduate to the MiGs and Mirages.
Beating a Soviet-era fighter jet off the line is easier than you might think. The Albatros weighs roughly 7,600 pounds, which takes a few seconds to get up to speed, even when using a turbofan jet engine. Meanwhile, the Leaf has a 214-horsepower and 250 lb-ft-of-torque front-mounted EV motor. The most powerful Leaf can reach 60 mph in 7.4 seconds and on to a governed top speed of 106 mph.
The L-39 has a takeoff speed of roughly 134 mph, which is confusing. We can clearly see the jet take off at the end of the battle. We can only assume Nissan removed the limiter and slapped better tires on the car.