First, download the .png version of the Ubuntu emoticons from the first link you have provided. Save them wherever you want, though here I will assume they will be in your Downloads folder. Extract after downloading by right-clicking the tar.gz you downloaded and selecting "Extract here".
Next, hit Alt+F2 and type in
gksudo nautilus. You will need to provide your password at the prompt. Once Nautilus starts, navigate to the
/usr/share/icons/gnome/16x16/emotes directory. You should see all of the default emoticons if you go to the right place.
Open your extracted Ubuntu emoticons in another tab or window, and create a backup of the originals (right-clicking to copy and then pasting back into the same folder should create .png's renamed as copies, which should be enough). Delete the original icons you want to replace, then copy and paste the new icons into the emotes directory. Lastly, rename them so that they have the names of the original icons. To test, start an Empathy chat window and try typing in your new emotes!
Note that the Ubuntu emoticons provided in that blog post are not a complete replacement for all of the default GNOME icons. You will have to pick and choose which ones you want to use, or you can create additional ones on your own as needed.