There are actually more than two types of quoting in bash. In addition to 'single' and "double there are also $'ANSI-C' and $"localized" quotations. For this problem I would have used the $'ANSI-C' quotation:
alias show_network=$'nmap -sn 192.168.0.0/24 | awk '/^Nmap scan report/{print ""; print; next}{print}''

Personally I find this a bit more readable. It might not be as portable but that shouldn't matter as the episode specifically addresses Bash.

Here are the expansions for the ANSI-C quotation in the Bash manual:
https://www.gnu.org/software/bash/manual/html_node/ANSI_002dC-Quoting.html