Assuming it is windows based, you can configure the firewall to block all other traffic. You will have to find and allow the DNS server also. You may also need to allow access to microsoft and the google update server so chrome and windows can update themselves.
Depending on how your network is setup, your local networking team could also put a block in place at a higher level. Then even booting off a USB stick won't get you addition websites.
First identify what you need to communicate with which is your dns server,dhcp server, gateway, and your 1 website. ipconfig /all should give you most of it. If you don't allow the additional IPs you won't access any websites.
You may not block 0.0.0.0 or 255.255.255.255 if you use DHCP
now create ranges. say you need 188.8.131.52,184.108.40.206,220.127.116.11
range 1: 0.0.0.1-18.104.22.168
range 2: 22.214.171.124-126.96.36.199
range 3: 188.8.131.52-184.108.40.206
range 4: 220.127.116.11-255.255.255.254
then combine them as shown below
from an administrative command prompt:
netsh advfirewall firewall add rule name="block all!" protocol=any dir=out remoteport=any remoteip=0.0.0.1-18.104.22.168,22.214.171.124-126.96.36.199,188.8.131.52-184.108.40.206,220.127.116.11-255.255.255.254 action=block