Let's start with a before/after to make my point
CTRL+SHIFT+P and look for
Package Control : Install Package
Type "Highlight" and take the first one which is available on Github too.
Close and re-open Sublime, select your text and right click, you can now choose between copy, copy as HTML and copy as RTF.
I prefer the monokai theme, you can change it under
Preferences > Package Settings > SublimeHighlight
To make it work in Word 2007, create a new html file, paste in it, save and import the file in Word :
Insert > Object > Text from file...
Should work in any software which took HTML text as input.