I just tested the game a bit, it occupied - depending on the content shown - between 200MB and 2GB of RAM. Nothing out of the ordinary and it also goes back down after animations.
But ... you are not getting a "OUT OF memory" error, just "memory".
There is always the chance that it's not related to your RAM at all, but to the stored game files. Try downloading the game again.
And make sure you DO have a swap file on your hard drive, some games depend on one being present, no matter how much RAM the PC has.