The seals should meet at the corners. I suspect your old weatherseal just shrunk over time, which is a relatively common occurrence.
thanks
Wow, amazing that it shrunk by that much.
Not sure I know how to get to the weatherstripping on the fixed windows.
When the manufacture installed the original weather stripping, they might have pulled or stretched it, which would in turn cause the weather stripping shrink back.
You will need to remove your fixed sashes to install the new weather stripping. To do that, most window manufactures have the stationary sash secured with clips. These clips are normally on the inside of the sash hidden by the inside window trim around the sash. I know Andersen and other manufactures use this set up, at least, so it's fairly common. It can be a little tricky, so if you've never done it before you might want to have a professional do it for you so as to not to damage the trim or the window.