Nice work! I would have done some things differently, but this is very readable.

Two recommendations for reading the file:

• Use the (z) and (Q) flags so that instead of using tabs to separate the targets, simply quoting each argument works.
• Instead of two independent lists, use an associative array with map[$link]=$target. Then you can check for duplicate links while reading the list.

linksfile=$1

typeset -gA linkmap

while read -r line
do
	# -- fields
	fields=(${(Q)${(z)line}})
	# -- link
	link=${(e)~fields[1]}
	# -- target
	target=${(e)~fields[2]}
	# -- check if we've already seen this link
	if (( $+linkmap[$link] )); then
		echo "'$link' targets both '$linkmap[$link]' and '$target', aborting"
		exit 1
	fi
	if [ -z "$target" ] || [ -z "$link" ]; then
		echo "Empty link or target provided, skipping"
		continue
	fi
	linkmap[$link]=$target
done < $linksfile

Then later, you can iterate over each key-value pair:

for link target in "${(@kv)linkmap}"; do
	...
done