If you look at the properties of the Start Menu Console shortcut on a 64bit system, the "Start In" field points to "C:\Program Files (x86)\LANDesk\LANDesk ServiceDesk\", and the Target field just says "LANDesk Service Desk", and is greyed out, as shown below:
This is because the shortcut was created by the Console installer, and cannot be changed.
Because of this it appears that the shortcut only points to a 32bit executable, though it's important to note that it does not specifically name "Console.exe".
When you install Console on a 64bit system an extra executable, Consolex64.exe, is placed into the C:\ProgramFiles (x86)\LANDesk\LANDesk ServiceDesk\ directory:
This is the 64bit version of Console, even though it lives in the 32bit Program Files directory.
When you launch the shortcut, it is intelligent enough to know which version to load, and a quick check of the processes in Windows Task Manager will prove this.