Hi Jimmy
I see from your web map's URL that you are using ArcGIS Online. (If you were using ArcGIS Enterprise, then that would answer the question immediately, because Story Map Shortlist isn't included in ArcGIS Enterprise). What I think is happening is that in your ArcGIS Online Organization's administrative settings, it is pointing at custom group of apps instead of the default group of apps to populate the App Gallery for people such as yourself using that Organization to create apps, and that custom group doesn't include Story Map Shortlist. You could see if your ArcGIS Online administrator could add Story Map Shortlist into that custom group. They could also add Story Map Cascade into there as well, which is another cool Story Map app I'm not seeing in your Gallery. Alternatively they could give you access to all the standard apps by reverting to pointing at the default group of apps, but there may be reasons only a subset of apps are being presents to authors.
There's some info about this here in the ArcGIS Online help: Configure map—ArcGIS Online Help | ArcGIS
Rupert