Very rarely there is a bug with the Playstore App. This happens when the play store app doesn't report that there are purchases and this can have multiple reasons(, most likely because you have multiple Google accounts on your phone). Please let me know if the following helped.
Try this:

1) Uninstall LocalCast

2) In a BROWSER on your desktop: Log in to the web interface of Google Play with the account you used to purchase

3) Install LocalCast from the web interface to your device
Don't let it open the Playstore app, but use the install button and choose your device in the browser.