By design, xDAI is a token that heavily tied with DAI on the Ethereum mainnet. In fact, the process of minting and burning xDAI is done, uncommonly for gas tokens, purely via a xDAI bridge that ensures the peg to DAI on the mainnet.
As such, xDAI is ntaurally a representation of an offchain (from Gnosis' perspective) asset, in this case DAI on Ethereum. Note that there is no hard peg guarantee; rather, the peg is maintained by the market thanks to the ability to bridge in both directions.