TehAlbi Okay, I figured it out for myself, and wanted to put my solution here in case it helped other people: First off, I had to go into my settings on Steam and go to "In-Game" and make sure that "Enable the Steam Overlay in game" is toggled ON, otherwise you will not get any pop-ups in game for the purchases. Next, the game will NOT take payment from you directly or redirect you to Paypal or anything else. It wants to take the money from your Steam Wallet. So you have to go to your Steam Wallet and add in the amount you wish to spend in-game into your Wallet. Then, when you go back into the game to make the purchase, it should let the purchase go through. A pop-up will happen where it asks you to pay, and the payment is made from your Wallet.
This was all totally stupid and it would be so much better if they just took payment directly through Paypal or your credit card, but whatever. At least I figured it out and hopefully this information will help others who are having the same issue.