Tezos has a soft-updating mechanism that works (roughly) as follows:
The network starts with a genesis block (that’s empty) and a genesis protocol (“protocol” here means “economic protocol”: the rules according to which a block is or isn’t valid, according to which smart contracts are initiated and acted upon, according to which transactions take place, etc.). This genesis protocol includes a public key.
The genesis protocol has no notion of coin, currency, smart-contract, etc. Instead, the genesis protocol knows a single operation: a protocol injection. As a result, the first block of a tezos-based blockchain is always the genesis block, and the second block is always a block with a single operation: a protocol injection.
The protocol injection for genesis requires the operation to be signed by the private key that matches the public key specified in the genesis protocol. And the protocol injection changes the genesis protocol to a new protocol. This new protocol specifies what constitutes a valid block to add to the chain on top of the block that performed the protocol injection.
In the Tezos blockchain, the protocol injected on top of genesis included notions of coins and smart contracts and a proof-of-stake system. It also included an in-protocol voting system to inject new protocols based on consensus amongst coin-holders. (The teos nodes are even capable of obtaining new protocol sources over the p2p network that supports the chain. This is so nodes can fetch the protocols, compile them, and dynlink them: you don’t need to update/restart your node to get the protocol updates.) However, this is protocol arbitrary: you can start a new chain and inject a different protocol on top genesis.
For example, you could re-implement Bitcoin (proof-of-work, coins, transfer, etc.) as a protocol that you inject on top of genesis. Your chain would have a genesis block, then a block that activates your own version of bitcoin, and then the blocks after that would be similar to what you would find on any bitcoin-like chain.
Of particular interest to you, the protocol you inject can have entirely different on-chain notions and operations (e.g., a TCG/CCG with no coins at all but a notion of ownership over cards and some way to transfer them). One of the thing you can change is the soft-updating mechanism: the newly injected protocol can use a genesis style of updates (a “dictatorship” where a single person controls the protocol) or it can even include no soft-updating mechanism at all (a “stale” protocol where you need to hard-fork if you want to make significant changes).
For this use case (of starting your own chain with a different protocol), you might be better off cloning the git repository, doing some minimal clean up, etc. This is because the tezos binaries include the sources for all protocols that have been used on the tezos main chain (just so you don’t need to get them over the network even if you can).
You might be interested in the following blog post about how to write your own protocol: https://blog.nomadic-labs.com/how-to-write-a-tezos-protocol.html