steam_api.dll should not be touched because it's the Steamworks version used for compiling the tool. And yes, sure it works. It just calls the Steam API.
Are you sure there is no steam_appid.txt file in the same folder? Maybe try it when you are running no games.
I don't know what else to suggest because they are just few API and I tested it with success on all my computers. I really have no idea why it doesn't work there.
OK so not touching steam_api.dll, tried on 2 other computers with 2 different accounts, steam running in background with no games started - same result.
No steam_appid.txt, only what was in the archive (api, .exe and .cpp).
Maybe my routers are blocking the connection? I'll try a direct connection when I get home.