I can't access your map via the URL you provided because it seems like your organization website (through ArcGIS Online) has disabled anonymous access. Thus, you need to sign in, even though your map is public. If you instead use this:
ArcGIS Explore Online probably could have handled this better, and prompted you to sign in. However, that's probably not what you want anyway, if you are sharing this with the public. In general, if your organization does not permit anonymous access, you should use the www.arcgis.com prefix to any URL rather than an organization URL.