You might need to re-install the Steam client. That file is not part of the 7D2D installation, so I don't think the usual "validate files" will work. Does the main Steam user interface work?
not 100% if you read the entire thread, some people still having issues. i didnt read anywhere in that thread where anybody trid to uninstall and reinstall steam.
so try as @Boidster suggests and uninstall steam and reinstall it.
Thanks for your suggestions but reinstalling didn't solve my problem. But ultimately, I found the solution that worked for me. I downloaded the steam_api.dll from this link: https://dlldownloads.com/steam_api-dll/ and replaced the older file with the newer one. Then, I rebooted the PC and then actually I don't have any problems till now.