When you click on their profile in the app, one of the items looks like a chessboard. Choosing that will give a partial archive. It is limited ... it appears to mainly be Daily games from what I can tell. Not sure if it has always been like that or is a bug.
Either way, the number of games that can be seen, is limited on the app, even in your own archive. Using the website is best for that.
I can't seem to find other player's game archives on mobile Android. I can see my own under "Play", and I can view other players profiles and statistics, but I can't seem to find past games like I can on browser. Thanks in advance! : )