The NATO planes are available to any NATO country to shift military equipment.
This includes the US.
It looks like it went into a holding pattern after crossing into the US possibly to avoid planes entering into or using the training ranges close to the Mexican border just to the west of the figure eight pattern it flew.
It's a North American T-6 Texan or in the UK it's known as a Harvard.
T-6 or the similar navy SNJ are often painted in odd schemes for filming to portray German or Japanese planes of WW2 or to put on a good show as a baddy in airshows.
Looks like only one blade on the prop got bent so it seems probable that the engine quit and the pilot stuck it down on the road as the best place to land.