Chrome's task manager doesn't appear when using the Shift+Escape shortcut keys

...but does work when selected from the menu.
There are (or used to be?) problems with some sites like GMail, however Shift + Esc didn't work for me anywhere.
As helpfully suggested by Bruce at https://bugs.chromium.org/p/chromium/issues/detail?id=317276#c15 , if you've got Intel Management and Security stuff on your machine then by default it will have usurped the shortcut.  Change it in the Intel settings.