I'm trying to setup incoming email for my Amazon EC2 linux box. Namecheap Private Email records for domains with third-party DNS My domain's DNS is managed through NameCheap. They have a private email hosting service.
https://www.namecheap.com/hosting/email.aspx
Will this enable me to have a webmail interface where I can send / receive emails from my domain?
I checked your domain and it does not have any MX Records setup. See screenshot below. That is the reason you are not receiving the emails.
Check this steps to set up MX Records for AWS Route 53 for your domain