Because you cannot deliver an index, these contracts pay cash equal to the difference between the strike-price and the exercise-settlement-value. Most broad-based index options are also european-style-options, which removes early-assignment and dividend-risk entirely.
In the US they usually receive section-1256 tax treatment, and margin for them is set under broad-based index rules rather than ordinary equity rules. Both facts change after-tax and after-capital returns for active sellers.
Example: you are short one index call struck at 5,000 on a $100-multiplier index. Settlement prints 5,012. You owe (5,012 − 5,000) × 100 = $1,200 in cash. No shares move, and nothing appears in your account except the debit.
Related: equity-option, cash-settled-option, european-style-option, spx-options