No. You're giving Sprint your iPhone 7, and paying $175 for an iPhone 8, which is yours to keep if you stay with Sprint for 18 months. You're basically getting a $525 value trade-in.
The way they're getting you to stay in leu of a contract is that your lease payments are $29.17 each for 18 months. Sprint will give you a credit of $29.17 each month for 18 months.
If you quit Sprint, the credits end but you still owe those $29.17 payments.
At the end of the lease, the amount 'paid' is 18 months x $29.17 = $525. For an additional $175, you can keep the iPhone 8 and do with it what you want. If you DON'T pay the $175, then you need to give the phone back to Sprint.