A portion of the trading fees are rewarded to sushi stakers yes. Sushiswap is a community focused platform with the goal of providing more value to sushi holders. In a sense, by distributing fees amongst SUSHI stakers, they ARE reinvesting in the project. This is roughly explained in two mechanisms.
- Sushiswap incentivizes SUSHI holders to stake their tokens on the platform with trading fee APY. This reduces selling pressure as SUSHI holders will want to stake their tokens to take advantage of the fee accrual.
- The reduced selling pressure drives positive price action, both increasing the value of individual tokens held by stakers and the tokens given as rewards by Sushiswap. This positive price action makes the LP incentives (provided in the form of SUSHI tokens) more attractive to liquidity providers, which increases the TVL of Sushiswap and decreases the slippage on trading these pairs.
All this together provides a net positive value to both SUSHI holders, SUSHI stakers, and the sushiswap team.