DevTools: [SSP] fix live edit of property values

The problem arises due to the fact that treeElement value is not updated
at the moment of keyDown/keyPress events. The "input" event should be
handled for the proper text value.

BUG=422928
R=apavlov

Review URL: https://codereview.chromium.org/650123002

git-svn-id: svn://svn.chromium.org/blink/trunk@183612 bbb929c8-8fbe-4397-9dbb-9b2b20218538