If an user without abusefilter-modify enters this page, he can see parts of the page, but can do nothing with it, so he can write into the input field, but not press any buttons to do somehting with that input. That's why I think either the page shouldn't be shown to users without abusefilter-modify permission or the check syntax function should work at least, because this function can be used in any other (for example private) wiki too with the same result. In the second case I think the tools link below the title of the special page should be shown to every user.
Customize query in gerrit
|mediawiki/extensions/AbuseFilter||master||+34 -33||Completely disable Special:AbuseFilter/tools for non-maintaners|