Over at the JFK Truth Be Told FB page, Jerry Dealey posted a big color photo of the gates with the diamonds on them. He wrote, "Hard to tell, but hinges appear to be on the outside, indicating it swung out."

In the still from the Martin film above it looks like the gates are closed but they're not.
When the gates are wide open they rest against the interior wall. The shadows of the diamond pattern on the gates can be seen being cast against the wall.
If the gates can swing outward they can also swing inward, as this is the position we see them in the above image.