A “game” implies non-productive or zero sum.
By definition, an arbitrage is not that. Any arbitrage is the result of an inefficiency in prices or the economy.
When someone arbitrages prices back to where they should be, they are performing a service that everyone else benefits from, and are rightly compensated for this. Now, are finance people compensated too much for correcting price discrepancies? If yes, then that’s another arbitrage opportunity!
But the question of what would be substantially different is easy. No arbitrage = no markets = top-down command economy. Check out North Korea, Cuba, USSR, the former Yugoslavia, etc. for what would be different.