Why does grass send out runners across concrete when there is soil immediately adjacent to the plant?

My only guess is that it’s natures way of preventing root over crowding plus it’s easier to find patches of ground that haven’t been sapped of nutrients.

Because the plant doesn’t know where the soil is, and sends out runners in random directions hoping to find a place to root.

Grass does not know what concrete is and sends out its spawn anywhere.

I think runners tend to extend laterally if they have lots of light, and vertically if they don’t. In other words, they are moving toward sunlight and away from other plants which are competing for water, light, and nutrients. So, on hitting concrete (which, as @ragingloli pointed out, they don’t recognize as such), they must just keep growing in the same direction. There are no other plants on the concrete to shade them, and it’s more reflective than soil, so it offers plenty of light.

“Does the plant have a vested interest in seeking out new lands if what it is growing in is substandard?”

Plants with runners have evolved to seek out new lands, on a small scale. This means that over millennia, it has been a more successful strategy for these plants to get away from where they are. Not so far that the environment would be completely different, but far enough away that they are freer from competition by other plants and their own parents. And far enough that they can get past obstacles like concrete, evidently.

Note that most plants do this at some scale, and for the same reasons – runners are one form of dispersal, seeds are another.

“Does the increased heat given off by concrete draw the plant in that direction?”

My guess is that light is a stronger driver, but heat might play a role if this is occurring in spring.

“Is it something as simple as that is the way the runner was facing when it grew? ”

Without reading up on this, I would guess yes – it may also have something to do with which direction they’re getting the most light from, or the direction of any prevailing wind. These can vary at small (leaf-sized) scales due to the height of surrounding plants or other things, so all runners would not necessarily move in the same direction.