This platform is designed for blockchain based games, but currently, their only application seems to be a rip off of Crypto Kitties that accepts TRON currency. Their website is confusingly barren, as is their social media, and this particular asset was one that had a tremendous overnight pop. Likely due to the announcement of their partnership with TRON, who experienced a similar bull run.
As far as blockchain gaming currencies go, there is a huge amount of them. They have many competitors in this space with far better branding and technology, when standing on their own, they don't seem very impressive.
However, they do have a crowdfunding option which could be interesting to amateur developers in the space who are looking to get their own blockchain based games online. They plan to deploy a digital asset trading platform for the games involved in their system, but other options such as Wax or Enjin may have the edge here. If you plan to make a Game.com investment, give much thought to both the competition and the lack of public information available on this mysterious company.
This asset can be purchased on quite a few exchanges. Interestingly, the highest volume trading pair if you want to buy Game.com is the US Dollar Tether pairing. Bitcoin is a close second though if you would prefer not to use this currency, as many are not comfortable with it for various reasons.
This asset is an ERC20 token, and that means you'll need a compatible Ethereum wallet in order to store them. There are lots of perfectly acceptable options for this. If you need a recommendation then you can consider using My Ether Wallet, Meta Mask, Coinomi's mobile app, or a compatible hardware wallet like Ledger or Trezor. Whatever wallet you choose, be sure to never keep your coins on an exchange, and always back up your wallet file or seed phrase in a safe place in case of disaster.