Why is Barker a suspect for Douglas' murder?

From the text:

“The open window, the blood on the sill, the queer card, the marks of boots in the corner, the gun!”
“Nothing there that could not have been arranged. Mr. Douglas was an American, or had lived long in America. So had Mr. Barker. You don’t need to import an American from outside in order to account for American doings.”

In addition, the shotgun was American.