My 1099-G doesnt have a box 1 (Unemployment compensation) but does have $629 in box 2 (state refunds). Im trying to report it, but 1099-G is only asking for box 1.

You are in the wrong place.  Delete out of here.  

To enter a state refund just type 1099-G or 1099-g (with the dash) in the search box at the top of your return and click on Jump To it.

OR Enter the 1099G under
Federal on the left side
Wages & Income at the top

Scroll down to Other Common Income
You might need click on Show More to expand the section

Then it's the first line for Refunds Received for State/Local Tax Returns - Click Start or Revisit
You do not want the next line that says Other 1099G Income

On the first screen check YES - Received a State Refund.

Enter the amount and continue on and after a couple screens, it will ask you a couple questions to determine if it's taxable. It may or may not be taxable. It is taxable if you itemized deductions the year it is from. If you took the standard deduction it is not taxable and you don't need to enter it at all.

To enter a state or local tax refund (Form 1099-G) -

Click on Federal Taxes (Personal using Home and Business)
Click on Wages and Income (Personal Income using Home and Business)
Click on I'll choose what I work on (if shown)
Scroll down to Other Common Income
-On Refunds Received for State/Local Tax Returns, click the start or update button

Or enter state refunds in the Search box located in the upper right of the program screen. Click on Jump to state refunds