Plenty of opinions in this thread, and not a single person with any real data or proof. Here is the best simplification I can possibly make.
Torque multiplication is created via the mechanical advantages of gearing. In a car, the drive line mechanical advantage is defined by transmission gear ratio * final drive ration/ tire size. Need a better picture, search in Wikipedia or "how stuff works"
Here is mathematical representation of that 3rd video. (Bigger number wins)
At 30mph, stock geared, 2nd gear = 1.78 * 3.07 / 27.2 = 0.201
At 30mph 4.10 gears, in 2nd Gear = 1.78 * 4.10 / 27.2 = 0.268 <<<<WIN
Obviously win by the geared car since its multiplying the torque by a higher number. However, on that same case, if the stock geared car would have been in 1st gear, this would have been the results at the start of the race:
At 30mph, stock geared, 1st gear = 2.66 * 3.08 / 27.2 = 0.300 <<<<WIN
At 30mph 4.10 gears, in 2nd Gear = 1.78 * 4.10 / 27.2 = 0.268
Let's keep the race going, at 60mph, the 4.10 geared car is still in 2nd gear, while the stock geared is also 2nd:
At 60mph, stock geared, 2nd gear = 1.78 * 3.08 / 27.2 = 0.201
At 60mph 4.10 gears, in 2nd Gear = 1.78 * 4.10 / 27.2 = 0.268 <<<<WIN
However, by 70mph, the 4.10 geared car has to shift to 3rd gear. Results
At 60mph, stock geared, 2nd gear = 1.78 * 3.08 / 27.2 = 0.201 <<<<WIN
At 60mph 4.10 gears, in 3rd Gear = 1.78 * 4.10 / 27.2 = 0.1.96
MORAL OF THE STORY: There isn't a "right" gear. There simply isn't a transmission ratio or final ratio that give the best performance at all speeds. It does not exist, its always a compromise. You will never see rock crawling guys using land speed record gearing, or vise-versa. Do your math, and pick the gear that's best based to suit your driving style or racing circuit. Period.