We process payments through Stripe, which is also used by thousands of other companies (many of them a lot bigger than Pleco) and offers state-of-the-art security; even we have no idea what your credit card number is.
With the payment methods above, we collect your email address from the payment form, so that's why you're not prompted to enter it here.
We also support payment by WeChat Pay and Alipay, but for those, we do have to collect your email address, since Alibaba/Tencent doesn't provide us with one.
Also, please note that Alipay only works for holders of Chinese national ID cards; if you don't have one, it's OK to have a friend make a purchase on your behalf, but if you attempt to make an Alipay payment to Pleco from a foreign-registered account it will fail. Our understanding from Stripe is that WeChat Pay currently does allow foreigners to make payments to other foreigners, but that policy could change at any time.
Note on email addresses: We use your email address to send you a confirmation email with your purchase details. We also keep it in a database so that you can log on to retrieve your order information in the future if you lose it. These are the only things we use your email address for.