I never view pics from a 3rd party site. Others are more trusting than I am.
However, I've attached, using Sevenforums paperclip, a snapshot of a full taskbar. Where there is a yellow and a red marker are arrows. By cliking on the down arrow I go to a display like you had.
Between your task bar and the system bar on the right-hand side, do you see a faint vertical bar with an up and a down arrow. That will switch you between you two and a full bar. this is a way that Win 7 handles more icons that there is space. I'll wager that if you reduced the number of icons, you would find that the overflow problem is gone.