I don't know if this has been covered, or not, but I figured it wouldn't be a bad thing. You can download the APK directly from BlueStacks without using the various AppStores, but it requires a little work. (Extra details added for those not Android savvy.)
1. Open BS and click the magnifying glass icon in the top right corner.
2. Type "Firefox" and hit Enter.
3. Select the install on "Firefox for Android." It'll search the stores, just select the first one you see. It's a 20MB download, so it may take a little bit if you're on a slower connection.
4. Once Firefox is installed, open it, and browse to "parallelkingdom.com.
5. Once the page is loaded, click the PC/Mac button on the right-hand side. Then the "APK" link, once that page is loaded.
6. BS will take over the download process from here, but you're not through, yet. Click (and hold) the top edge of BS and drag down. This will show you the download progress.
7. Once the APK is finished downloading, it will say "downloaded successfully." Click on that, and install the APK.
8. Load the game, login and enjoy!
Hope this helps anyone who may be having problems running the downloaded APKs manually.