This is 100ft Robot Golf, which is coming out for PlayStation 4 and PlayStation VR later this year.
Developed by Seattle-based team No Goblin, its name pretty much explains the whole game. Players control giant robots as they seek to make par, while destroying anything that gets in the way. No Goblin's previous game was Roundabout, a Crazy Taxi-style driving game featuring a constantly rotating limousine.
Based on a playthrough at the Polygon offices earlier this week, 100ft Robot Golf looks strongest in competitive mode, with up to four players split-screening their way through the links. Strategies include attacking rival robots, throwing stuff down in their way and jumping in front of balls in flight.
There are a variety of worlds including a city, seen in this video, as well as an underwater world and the moon. According to No Goblin, the game could come out on other platforms at a later date.
Disclosure: Subsequent to the making of the above video, it was announced that the commentary track in 100ft Robot Golf is being provided by My Brother, My Brother and Me, a popular comedy podcast featuring three McElroy brothers, two of whom also work for Polygon. More here.