Whether you fall on the "games" or "no games" side of baby showers, there actually are a few way to still incorporate this traditional activity into your virtual party.
Lalo has a series of bingo boards that can be downloaded and randomly distributed to guests before the party. Guests can cross off items as gifts are being opened, and whoever gets a bingo first is the winner.
You can also play an online version of "Baby Price is Right." Just gather 10 or so baby items (bottles, dummies, etc.) and have guests guess the price during the party. Whoever gets the most correct answers wins. There are plenty of free printable answer sheets online (Pampers has one, along with many other baby shower games) if you want to make it easy for guests to keep track of their answers. After the party, you can ship or drop off the items to the expectant parent.