Here is the process I used based on the documentation guide found here:
Create the portal object by providing the URL string to the portal. In the example below, the public map is accessed from ArcGIS Online (www.arcgis.com):
//construct the portal from the URL of the portal Portal portal = new Portal("http://www.arcgis.com");
Construct the portal item object by providing the portal and the item ID string for the map:
//construct a portal item from the portal and item ID string PortalItem mapPortalItem = new PortalItem(portal, "e229d715f7ca4fa980308549fb288165");
Pass the portal item to the map constructor:
//construct a map from the portal item ArcGISMap map = new ArcGISMap(mapPortalItem);
However, I realized this would not work (the map would never load and display) whenever I passed an item ID for a Web App, but it did work when I passed in an item ID for a Web Map. Could anyone further explain why PortalItem does not support the display of Web Apps?
Web Apps are not supported because the ArcGISMap is the runtime corollary to a Web Map. A Web App is an HTML/Javascript standalone application and not something that is supported within the runtime SDKs.