After switching off all virtual mouse and controller mapping options in Shield Tablet K1 2015 android settings for Shield Controller 2015 and then use trackpad on controller as much as possible gives good mouse behaviours. Touchscreen on tablet helps out too especially when Steam Input can not apply configurations or when in LS client GUI out with skycomputer desktop.
Basically disabling virtual mouse on device and using trackpad on controller instead of right joystick fixes a lot of things. None of these options on SATV! afaik