That would indicate there is an background service on your computer that prevents you from installing a new version of WinPcap.
The easiest step is to start your Windows PC in safe mode and check if the updated WinPcap installer can remove the old one.
Realize that the WinPcap software hooks into your software Windows requires, else it won't be able catch network traffic. This software needs to be able to work on a level very close to the networking hardware in your computer. Windows is not fond of this kind of software and required you to reboot the first time you installed it.
So, while I understand you don't like to reboot your computer, with installing and removing this kind of software you must. Because if you don't, you'll quickly find yourself in a mess similar to this one.
When in safe mode, if the updated installer cannot get rid of the old WinPcap installation, you will need to find out which background service blocks the installation. Process explorer
(part of the Sysinternals Suite) will be a great help. Dependency Walker
is another very good investigation tool. While I don't think these tools are hard to use, you might think otherwise. Please read their online manuals, because you will be the one doing the legwork.
Next time you go on an "adventure" like this, Use a free tool such as RevoUninstaller
(scroll to the bottom of that page to find the freeware version) for removing software from your computer. While the Windows control panel gives you the illusion of removing software, it often doesn't. With a tool like RevoUninstaller you will be amazed about the amount of crap that remains after Windows reported it removed software from your system.