Does the browser object in neobook support HTTPS webpages?
You can certainly display secure https websites with NeoBook's browser. Since the browser is based on IE11, you could argue that it's less secure than other browsers. However, I believe that Microsoft is still providing security patches for IE11.
Many popular websites are still http, so unless you're collecting personal or confidential information from your visitors I'm not sure why you would need to pay for a SSL certificate. Also, https sites are generally slower than http sites.
It seems like Google (as basically a search monopoly) should be neutral with regard to website appearance, content, etc. They should present results based on relevance and popularity rather than their own arbitrary conditions. Let web users decide what they want to see. If users prefer ugly mobile sites or https sites, then those sites will be more popular and naturally appear at the top of searches. Maybe adding these expensive burdens is a way to get rid of the little guys.