Jordi Amat's own goal came before the rain, strong winds and lightning forced the players off in Virginia.
Substitute Anthony Grant put the game beyond doubt as Swans boss Francesco Guidolin made sweeping changes to his starting line-up.
Swansea beat Charlotte Independence 4-0 in their first tour game.
New Swans defender Mike van der Hoorn made his debut after joining from Ajax at Charlotte.
Guidolin was unconcerned with the outcome and praised his players for their "hard work".
He said: "It's normal in pre-season to have performances which are up and down.
"I think the players have worked very, very hard in this period and in this game as well.
"It was an good test for us because it is important at this stage to get used to the rhythm of games again.
"I am not worried about the results."
Charlotte Independence 0-4 Swansea City
Richmond Kickers 2-0 Swansea City
Bristol Rovers, Saturday, 23 July 15:00 BST (Memorial Stadium)
Swindon Town, Wednesday, 27 July BST 19:45 BST (County Ground)
Wolverhampton Wanderers, Saturday, 30 July 15:00 BST (Molineux)
Stade Rennais, Saturday, 6 August 15:00 BST (Liberty Stadium)
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Swansea City lost the second and final game of their pre-season United States trip in a match disrupted for 95 minutes by a storm.