Assuming that at this moment, all inside hosts have permission to access all external hosts on any port, you need to add two rules:
- allow access from the inside host to the external host (not a domain) on port 80.
- deny access from the inside to that external host.
If that assumption is not correct, you need to provide more useful information.
EDIT: I see you added the fact that there is no global NAT pool almost as an afterthought - so does this mean there is currently NO NAT configured from inside to outside, for this inside host ?
If that is the case, you need to configure it; the easiest way is to add a static policy NAT from the internal host to the external host, on port 80; you can use the ASA interface as the translated source address.
This would obviate the need for the access rules above.