I couldn't get any of the above methods to work on Windows 10, but I think I've found another that does:
Install 7-zip if you don't have it already
Download the LDD installer from Lego
Right-click on the LDD installer file (i.e. setupldd-pc-4_3_11.exe) then select 7-Zip / Extract to "setupldd-pc-4_3_11\"
Navigate into the setupldd-pc-4_3_11 folder
Right-click on LDDSetup.exe then select 7-Zip / Extract to "LDDSetup\"
Navigate into the LDDSetup folder
Double-click on LDD.exe to run the application