I upgraded the plugin, and now SketchUp automatically show the dimensions, without click menu item and hotkey, and this feature can be disabled if it interferes.
Download link:
Dimensions Tool
Menu:
Tools > Dimensions Tool > Get Dimensions - old functional
Tools > Dimensions Tool > Auto Display Dimensions - checked menu item, which switch auto get dimensions functionality after select object.
P.S. Let me know if you need to modify the algorithm and move plugin to another menu for the convenience.