This project is a scalable blockchain that's intended to be used for the distribution of games and social applications. By utilizing the blockchain, they plan to allow even hobbyist developers to distribute their games on an even playing field. Developers and players will be able to use monetized tokens that can be traded throughout games or even cashed out at a later time.
This allows for the creation of "scarce" collectibles that can attain real-world value. In order to combat the issues which are inherent with Ethereum itself, this ERC20 token runs its applications on side chains to avoid clogging up the main network if a game gains popularity too quickly.
While it's unlikely that big game developers will ever adopt a system such as this, they are not the key audience. The main users will likely be those small-scale developers that may be comprised of only one or two people. Players can also trust these games as it's run on an open source software, and everything is secured by smart contracts. It's an interesting concept, and in the future your Loom Network investment could usher in a new era of gaming where people may have to accept that digital items have value.
You can only buy Loom Network on just a few exchanges. However, there seems to be ample trading volume for both Bitcoin and Ethereum, which will make it easy for you to make a swap. Unfortunately, most of the volume seems to be on one exchange, effectively reducing your options.
This is an ERC20 token, and that means you can store it in any wallet that is compatible with various Ethereum based tokens. The most popular choice for this is My Ether Wallet. However, if you'd prefer a cold storage option for added safety, then you could check out the Ledger or Trezor hardware wallet options as well.