Looking for positives, this could be Milwaukee County Stadium, home of my dad's Braves from 1953 to 1965. Wikipedia supplies a picture postcard of the original concept with no outfield stands and large parking lots beyond, roughly matching what we see behind Logan. A roof-mounted American flag would further sync up to the card, but no stadium pictures I could find had one. Summary: encouraging, if not 100% certain.
The card-and-stadium conversation reminded me of a cool contemporary set, the 1955 Topps Doubleheaders. Each one featured a main image with "reusable legs," inviting collectors to fold the top half over and see the alternate player. (Card backs included brief stats for both.)
Interesting enough on their own, Topps' Doubleheader artist upped the ante by including contiguous stadium scenes on the background of consecutive cards. A turn through the Net54 baseball forums turned up three different scans that show off this creativity.
First, an uncut portion shows the flow across a half-dozen players. (Follow the link to see larger versions.)
Second and third, check these scans from a Baseball Cards Magazine article by Bill Bossert in 1984. Note how each line of players flows across stands, a batting cage, and other stadium features. The full set includes several actual parks, including Yankee Stadium and Fenway, with 5 or 6 backgrounds spanning the full "image."
Modern sets go for puzzle backs and other card assemblages over this elegant idea. Anyone know of another set that combined backgrounds in sequence?