If you are having trouble downloading an application to your NOOK, where it seems to be stuck in a download cycle but never really installs, then it could be that your device doesn't have enough memory space available for downloading and installing the game. We recommend you 'Archive' or 'Move to NOOK cloud' some apps to clear some space (typically you will need around twice the amount as the applications file size) and try installing the game again.
Please note that archiving books may not help as these are stored in a separate partition.