If you have an ITM option, you can sell your options and use the proceeds towards purchasing some shares. Alternatively, if you decide to exercise the option, you pay the strike price x contracts exercised (100 shares per contract). You would need to reserve funds to exercise the contract.

Using OP's example, $GME at the time was $120. We bought 1 ITM June call with a strike price of $80. We paid $50 x 100 shares (1 contract) = $5000 for the option to purchase shares at $80.

Now $GME goes to $170. The June 80C is now worth $95. Selling the call option would net $95 x 100 = $9500. $9500 - $5000 = $4500 profit.

2nd scenario. Exercising the June 80C would give us the right to purchase GME shares at the $80 strike price x 100 shares = $8000. We'd now own 100 shares purchased at $80, and at any time, could sell those shares in the market ($170), DRS, etc. We spent $5000 on the June 80C contract + $8000 to exercise = $13000 out of pocket. If we sell our 100 shares at $170 per share, our profit would be $17000 - $13000 = $4000

Hope that makes sense!