During this era it was common for the outfielders to leave their gloves on the field when they were at bat. You can see them in this photo.

After looking at Marc Okkonen's book, Baseball Uniforms of the 20th Century, I think the visiting team may be the St. Louis Browns. Other than the Naps, who are the home team here, the Browns were the only other team in the American League who wore a gray road uniform with lettering printed across the shirt. I may be wrong, but two of the visiting players appear to have this kind of lettering on their uniforms. All the other teams carried an initial (or two for the New York Highlanders) or wore navy blue uniforms on the road. The stockings on this team are also consistent with those worn by the 1908 Browns.

Home of the Cleveland Spiders, Cleveland Indians and the Cleveland Buckeyes.
The field was built in 1891 and part of it still stands on the corner of E66th St and Lexington in Cleveland.

In 1908 the Cleveland AL franchise was nicknamed the Naps in honor of star player Napoleon Lajoie. It would not receive the Indians nickname until 1915.

I'm having a hard time determining the visiting team as the jersey details are hard to pick out and compare to the Baseball Hall of Fame's uniform database. I do however see a tall, thin man in a suit and straw boater in the visitors' dugout; that makes me want to believe it's Connie Mack and his Philadelphia Athletics who are playing the Naps.