To be clear, the cable ISP only provides one IP address. A router of the sort that Linksys would make obtains that address and works as a intermediary for the rest of the computers on your network, by providing fake IP addresses to those computers and translating their traffic to the real IP address.

Using one of these would work because your computer and your empeg would both get compatible addresses from the router, making it easy for them to communicate with each other.

The hub bought is nothing more than an ethernet distribution device. It is basically a Y-splitter for ethernet. But there's still only one IP address provided by the cable modem, which is acquired by the computer; the empeg will get a pseudo-random IP address about which the computer and cable modem will have no information because the IP address has already been taken. In fact, it's possible that if the empeg was booted while the computer was off, it might get that IP address, but cable ISPs often make sure the given IP address is only given to a single ethernet interface, so that might not actually happen.