According to ye olde standards, a computer would respond to every connection attempt with, typically, one of three responses:
- Application banner indicating that a service is listening and which service
- ICMP Port Unreachable - indicates that nothing is exists on this port
- ICMP Administratively Prohibited - indicates that your system is not allowed to access this port
By those rules of etiquette, one would expect firewalls to respond with the 3rd kind of message. However, nowadays one typically expects firewalls to drop packets without sending a response. This is what Gibson is referring to as "stealth mode".
Unfortunately, the Shield's Up website is fairly dated. The advice and analysis makes assumptions based on the late 1990's Internet. At that time it may have been a reasonable assessment, these days I wouldn't give it much credence.
A host based firewall has been included and enabled since Windows XP SP2. So, whether you realize it or not, you do have a firewall running. However, the more likely culprit is your home router. Those require special configuration, called port forwarding, to pass unsolicited traffic from the Internet to your computer.