I'm not sure what your question is. Do you want to save the log on the website dom.retrobox.eu or do you want to save it on your own computer?
In the first case, the answer is "no", but you can always go to the same webpage again, and the log will be colored again for you. AFAIK, Goko doesn't delete old logs, so this will always be possible.
In the second case, right click the page and select "Save As".