You might not have a genuine Verizon G2. Possibilities include (1) your G2 is genuine but isn't from Verizon, but instead was intended for the Chinese market (and therefore didn't have Google Play Store preinstalled because the phone isn't certified for Google Play), (2) your G2 is genuine but someone rooted it and installed a Chinese ROM, or (3) you have a fake.
Go to Settings>About Phone, and tell us what the Model Number is.