Whether Stripe requires a merchant's website to be served over HTTPS?

I asked it to Stripe support.

I have got an answer from Stripe:

To process payments online, you must be fully PCI complaint.
Part of being fully PCI compliant is serving payment pages using TLS, so we do require all users to do this.

So, the answer is «yes».

You can found an additional information here: https://stripe.com/docs/security

It looks like the HTTPS requirement is legal only, not technical.
It means, that you can use HTTP in the test mode, even for webhooks (I have not noticed any technical restrictions for it), but when you will apply for switching your Stripe account to the live mode, your website will be reviewed by Stripe, and they will require your website to be served over HTTPS.