The firewall rule is blocking IP addresses which start with 173.194.55 or 206.111 from making connections to your computer.
The article suggests that these addresses belong to CDN servers which is basically a cache that may be geographically close to you. This means that the YouTube servers don not have to send the same information over and over again.
The reason that the article gives for this causing a slowdown is that your Internet provider may be slowing down traffic from these addresses. Therefore blocking them will force the stream to be sent directly from YouTube's server which the Internet provider may not be slowing down traffic from.
If you have were not experiencing slow streaming before or have not seen any benefit from adding this rule, then I suggest you disable it as it could also slow down your connection if the CDN servers are not being slowed.
Additional Information About the Command
netsh command is used on Windows systems for viewing and changing the configuration of network components and services. For more detail on the tool you can look here.
advfirewall firewall add rule part tells it to add a rule to the firewall.
name="MITCHRIBARYTUBE" part defines a name for the rule. This can be anything you like; to make it easy for you to recognise later.
dir=in specifies the direction of the rule, in this case inbound. This mean that this rule applies to computers trying to connect to your computer as opposed to when you connect to other computers.
action=block tells it to block any traffic that matches this rule.
remoteip=188.8.131.52/24,184.108.40.206/16 tells it that this rule applies to traffic where the other computer involved has an address starting with either 173.194.55 or 206.111. The /24 and /16 tell it how much of the address to use. There are eight bytes for each number between the dots so /24 tells it to use the first three (24/8) numbers (173.194.55) and /16 tells it to use the first two (16/8) numbers (206.111).
enable=yes simply sets the rule as enabled.