Schoening
I'm interested to know why you have 'Multiplayer' in the topic title. Are you thinking of the situation where a player adjusts his/her window size independently of other players?
Even in that situation, there could not be any effect on the movement speed of his/her own player.
The reason is that play is taking place within the canvas/layout, which itself is within the browser window, whose resizing necessarily has no effect on the predetermined size of the canvas/layout within it.