As TriangleRocks stated there is a version that has the three dots, this appears to only be in the tablet version of Touchdown from looking at the pictures in the Google Play store.
I found two other options in my research that worked for users at my location.
The first and simplest which people reported working for some apps, but not conclusively for Touchdown, was long holding the back button.
For these older apps that you are unable to access the in app menu. You can enable a soft menu button by doing the following: Settings>Accessibility>Dexterity and Interaction>Assistant Menu
This will give you a set of soft buttons, one of which is "More Options" or Menu essentially.