Zsh says "no matches found" when trying to download video with youtube-dl

Try quoting the URL, e.g.

youtube-dl '{video URL}'

in your notation, to avoid possible interpretation of special characters in the string.

This was already mentioned in the comments, but it deserves its own answer:

autoload -Uz bracketed-paste-magic
zle -N bracketed-paste bracketed-paste-magic

autoload -Uz url-quote-magic
zle -N self-insert url-quote-magic

This causes pasted URLs to be automatically quoted, without needing to disable globbing.

Place the above snippet in your ~/.zshrc file to persist this setting for future terminal sessions.

You can disable globbing for all commands with:

unsetopt nomatch

You can put it in ~/.zshrc.