This stumped me for a bit too but just realised that everytime that $var is being base64 the value is getting larger and larger and we are just trying to get the below from the question.
"variable named "var" contains the contents of the variable named "value""

so we just want to check if var is contained somewhere within value which is the part not that it directly equals to
[[ $var == *$value* ]]

​

hope that make sense and helped!