Translation:It is forbidden to go to this place.
No, it doesn't most of the time, as you can point out the meaning by context (in the case of απαγορεύετε/απαγορεύεται it is obvious most of the time). If there is an ambiguity because of same sounding words (for example οι φίλοι μου=my friends, η φίλη μου=my female friend), it's not unusual for the speaker to say on his own οι φίλοι μου με όμικρον γιώτα to denote that he/she means οι φίλοι and not η φίλη.
Is there some grammatical rule being applied to this mark?
In diphthongs (where two vowel letters make one sound), the accent mark goes on the second vowel letter.
For example, πηγαίνω, where αι makes just one sound.
This spelling practice continued with αυ and ευ even after they started being pronounced /av ev/ rather than /au eu/.
(Putting the accent on the first letter would mark the two vowels as belonging to separate syllables, as in άυλος "incorporeal", pronounced a-i-los, from α- "a-, in-, non-, un-" + ύλη "matter".)