@bennessb The one it replaced was a much more Art Deco retro building, which sadly I can't seem to find good photos of, but did just discover that Greyhound once had many beautiful Art Deco stations across North America.
The building shown above has its days numbered now, too. Greyhound just announced they will be moving their Edmonton terminal adjacent to the VIA Tterminal near the old City Centre Airport (now Blatchford, a new community under development). The old building will be demolished and replaced with more ICE District development that will include a new condo tower (Tower "B"), Cineplex Theatre, a major grocery store, and additional retail.