The DOGE are "destroyed" by sending to them to an address for which no one knows the private key. The address is DDogepartyxxxxxx... which is clearly human-generated. Calculating the corresponding private key is equivalent to breaking Elliptic Curve encryption (and if someone can do that, the whole bitcoin ecosystem comes crashing down in flames -- because they could compromise any and all accounts, not just this one).

Once XDP is created, there will be an XDP/DOGE market on DogeParty, just as there is an XCP/BTC market on Counterparty. Using this decentralized exchange, you will be able to trade your XDP back for DOGE if you desire. (This feature is currently disabled in DogeParty but will be re-enabled soon)

DogeParty/CounterParty is considerably more powerful than the underlying currency. It has an internal, decentralized market for tokens. You can issue dividends. You can place bets and broadcast information. For more, read about CounterParty. (The DogeParty code is identical, save for renaming BTC -> DOGE and changing the burn formula slightly)