Welcome to Android Central! Is this some kind of Android TV stick you plug into a TV? Did it come with Google Play Store preinstalled, or did you have to install it manually? If the latter, it might not be compatible, since the device probably isn't certified for Google Play.
If it did come preinstalled, then try going to Settings>Apps>All, select Google Play Store, and Clear Cache/Clear Data, then Force Stop. Do the same for Download Manager. Now try again.
If that doesn't work, try going to Settings>Accounts-Google, select your Google account, and remove it completely from the phone. Then add it back again, and see if that helps.