So you're trying to send an email to
zach@thezach.net, and exim is telling you that it has no idea where to send that email.
1. The public DNS records for thezach.net shows that the one and only MX record for your domain thezach.net is smtp.digitalexample.net. Is this the email hosting company that you're using? If so, is smtp.digitalexample.net the correct MX record to be using?
2. Does your server think that its hostname is thezach.net? The first line of your log suggests that it does. In that case, exim will think that
zach@thezach.net is a local email address. It will try to deliver the email to the mailbox of a local user named zach. Not what you want! (I'm assuming that you don't want to use your Linode to read emails, since you're outsourcing your email to another company.) Change your hostname to a subdomain and try again. You'll also need to go through exim's configuration files to update the hostname.