Why a gate if a cow can get out anytime it wants?

The rack you see that the car drives over, the bridge itself that is - IS in fact a Cattle gate.

I will privledge you with learning about them here :

http://en.wikipedia.org/wiki/Cattle_grid

A cattle grid – also known as a stock grid in British English; cattle guard in American English; vehicle pass, Texas gate, stock gap in the U.S. Southeast;[1] or a cattle stop in New Zealand English – is a type of obstacle used to prevent livestock, such as sheep, cattle, pigs, horses, or mules from passing along a road or railway which penetrates the fencing surrounding an enclosed piece of land. It consists of a depression in the road covered by a transverse grid of bars or tubes, normally made of metal and firmly fixed to the ground on either side of the depression, such that the gaps between them are wide enough for animals' legs to fall through, but sufficiently narrow not to impede a wheeled vehicle or human foot. This provides an effective barrier to animals without impeding wheeled vehicles, as the animals are reluctant to walk on the grates.

Why a gate if there's a cattle grid?

That makes the gate even more surpufluos. Most cattle grids dont have fences or gates over them, and they keep the cattle inside and the roads gate-free. This gate is cool from an engineering standpoint, but I dont know what sort of animal its supposed to keep in(or out). an animal that would be light and agile and fearless enough to step on the grid without opening it(like a cat) could easily also traverse that fence. Animals heavy enough to open the gate wouldnt cross a gateless grid either..

ok

Kind of.
Real cattle guards require a pit below them so the animals can see their legs will fall through. This doesn't have that. Cows can be fooled with just white lines across the road. Some animals see better, so some animals would never try to cross the lines, but some would. Having the fence there discourages them from trying, since it's just more fence why bother (said the sheep). Maybe this field is used by differing animals that need different barriers, and this gate fits all the bills?

It's not powerless. It's powered by the car.

Maybe pressure operated wooden articulating gate?