It would quickly turn into a hellscape. As some comments and answers already explained, each teleportation would add energy to the system.
As already said, if you had a bowling bowl falling in the air, it would accelerate up to a point where the acceleration cancels out with air friction, reaching terminal velocity.
But this is much worse here, since it is the air itself that is moving, it has no "air friction" working against it, so the only thing that slows it down is not air friction, but friction against anything that isn't moving in the same direction. 621
As things like dust start to move with the wind, they contribute less to friction, and help erode everything else faster, which reduces the amount of stuff that slows the air down.
Unless there is no "ceiling" to the world, then I guess the atmosphere would spread out and "climb" as it accelerates, spreading thinner and thinner. If a particle has enough horizontal speed it could "do a lap" around the world fast enough to counter its own vertical fall, then, the upper layers of the atmosphere would be in low enough gravity, and encounter no resistance against the void, so that it could keep climbing this way indefinitely, leaving room for other particles below to go through the same process.
But if there is a ceiling high enough that there is no "chokepoint effect" with stuff on the ground (which would still produce heat, it would go the same way but it would happen much slower as the wind isn't as free to accelerate), then the only thing slowing down the wind would be stuff on the ground, dust in the air would only slow it down a bit by hitting against grounded stuff, but the ceiling would probably be high enough (probably doesn't need to be very high for that) that the upper parts of the atmosphere can keep accelerating, only getting "second-hand drag" from the air below. But as things keep eroding, more particles enable more erosion, until a point is reached where enough stuff has eroded that the whole world can cascade into an infinitely accelerating cyclone, definitely turning into, as a comment said, some plasma soup. 513