I stopped archiving finished games some time ago, and now My Games page is messy.
With more than 200 games, some of older games are on page 52, some on page 46 etc.

If I archived them one at the time it would have taken ages, because after each archiving, I am brought back on page 1 (one of site's bugs).

Is there a tool in which I can mark games and archive for example whole page at once by one click?!

Use the Manage Games page, tick all the relevant boxes, then do a bulk Move. I usually do it one screen at a time but you may be able to do more depending on your setup.

Thanks.