Is this the right approach?
I assume gifting someone one else money is only good to be used on the site. Then yes that is one way to go about it. Except maybe not using paypal.
Using paypal to send money into my account on your site is fine but as for using it for your site's merchant account/business I wouldn't do that. PayPal is a monster which has gobbled up other's money in the past or held it for long periods of time. They hold a rolling reserve in case of chargebacks as well. I wouldn't use them unless I was selling tangible physical goods. Look into alternative payment/merchant solutions. Speak with a real bank also helps as a lot of them provide internet services too.
Legally, are there any problems?
There may be depending on your site, physical location, business model and/or merchant account. Read all the policies, terms of service and disclaimer docs on paypal (or similar merchant account), read them all. Search the net for similar businesses who take money and hold it (flattr and kickstarter comes to mind) and see if you can figure out how they do it. Try finding some free info or stories about what they went through and why they made their choices and it should steer you in the right direction. THEN when your feeling like you got enough free information call and speak with a lawyer and get legal advice specific to your location and business.