I hit this on a new W10 machine and tracked the issue down to the newer W10 builds silently swapping the Windows Scripting Host path for "compatibility" which causes that compatibility error.
If you go into Start > Cisco ASDM-IDM Launcher > right click the launcher and go to More > Open file location
Then you'll be looking at the shortcut to the ASDM launcher, right click it and go to Properties and look at the Target. You'll see a long path to wscript.exe - change this to C:\Windows\System32\wscript.exe (leave the invisible.vbs run.bat on the end as these scripts are used to open up ASDM). After changing this I was able to launch ASDM fine.