Can FME can generate runtime geodatabases? Is this different to a FGDB?

Presumable it's this ".geodatabase"? https://developers.arcgis.com/android/10-2/guide/supported-geodatabase-formats.htm

I don't think FME can yet. Perhaps there is a way to use Python (arcpy) to convert a FileGeodatabase into one but examples looks like you actually need an esri mxd file rather than a geodatabase (https://desktop.arcgis.com/en/arcmap/10.3/tools/data-management-toolbox/create-runtime-content.htm).

It looks like the "runtime" database is based off of SQLite - so you could try to create an SQLite database and see if that works (unlikely).

GeoPackage is also based on SQLite so you could also try this too. Depending on the application Geopackage may be supported anyway.