If you downloaded and used an installer outside of Steam, you've downloaded and installed the standalone (website) version. You will need to uninstall it, as it does not use the Steam client for it's licensing - rather, it's looking for a registration key (which if not provided will revert to the VoiceAttack standalone trial).
Next, you'll want to open up your Steam client and install VoiceAttack from there. That will usually install VoiceAttack in the C:\Program Files (x86)\Steam\steamapps\common\VoiceAttack folder.
Inside that folder, you'll find VoiceAttack.exe. If you run VoiceAttack at least once with the Steam client running, VoiceAttack will pair itself up with your pc and you don't even need the Steam client from that point on. You can then set the properties of the VoiceAttack.exe to run as admin, or use the internal setting on the Options > System/advanced tab ('Run VA as an administrator').