HI Alex
The National Parks Timeline is a custom app we created from scratch: it doesn't use one of the Story Map application templates. We create these custom apps to try out different approaches and designs that might eventually be turned into templates or incorporated into templates, attract new audiences to our tech, and see what our developers can do!
There is a configurable app built into ArcGIS Online for working with time-based data that may work for what you'd like to do. It doesn't look the same as the NPS Timeline but see this blog post for more about it:
Using the Time Aware configurable app template | ArcGIS Blog
Another approach for showing change over time in a story map is to use the Story Map Series template and create a different tab or bullet for each time period you want to show. This is easy to set up and very flexible: each tab or bullet could show a different map or a different layer and/or extent on the same map, with narrative text and images too. Here are a couple of examples:
https://geoscience-au.maps.arcgis.com/apps/MapSeries/index.html?appid=72ad590cc9364e41b06907406bb771...
http://esrica-tsg.maps.arcgis.com/apps/MapSeries/index.html?appid=bd7ddfd489b749cf9beb25b5786a8031
Rupert
