The intelligence in our product for removing competitor software is static; meaning, if the package can't do it now it won't be able to ever until we release an updated package.
The opportunity for us to do that is when we post patches and repost the full install package too. The file uninst.ini is where the logic is found, and a supporting file, uninst.dll, is often needed too for handling special removal requirements.
If we had a PER system up and running I'd suggest submitting your request there. But in lieu of that, best I can do right now is suggest posting the details of the Kaspersky product here and I'll share the post with Product Management.
If you can, include some Uninstall key info from that product. Description, UninstallString, DisplayVersion... all found in a key under here somewhere: HKLM\Software\Microsoft\Windows\CurrentVersion\Uninstall\
I strongly suggest removing ENS 10.1 then using the Kaspersky Removal Tool to cleanly wipe off the KES & possible Kaspersky Network Agent off.