That is because the execution policy on your system is set to restricted. I forgot that this is the default, sorry about that. Also the script needs an update, because gelbooru changed their auto complete url.
Execution Policy:
If you want to run it and don't want to change the system settings to allow all scripts to be run (which I would not advise if you do not need it), then create a .bat file (e.g. start.bat) in the folder with the start.ps1 script.
Open it with any plain editor like good old notepad and paste this script:
powershell -executionpolicy RemoteSigned -File "start.ps1"
Which will set the execution policy for this one instance of powershell and make the script runnable.
Update:
Here is the updated version of the script to accept the auto completes in a JSON format.