This should be brought to their attention, it can have serious effects on how others interact and play the game. I have had the same exact problem with the login screen itself, and when I log into the client similar difficulties arise, when playing draft games it would be impossible to see the other team’s picked champions. Because of this I’m afraid of participating in ranked and other normal draft games. fortunately I have found a solution to this;
http://boards.euw.leagueoflegends.com/en/c/alpha-client-discussion-en/Nj7GMlux-new-beta-client-doesnt-fit-my-screen
The link above has a small conversation about this issue, and because the problem was considered resolved the conversation was closed.
Apparently, you can resize the client using the Crtl key and the '-' key or the Crtl key and the '+' key to make the client smaller or larger in order for it to fit properly on your screen.
it seemed to work well for me without any problems so I hope this works for you.