The "head" of the dinner table is usually the place of honor, or the place where the most venerated/respected member of the party sits. In a family situation, usually the father sits at the head of the table, and mother at the "foot," or the opposite end, which subtly indicates that she's "second-in-command." Of course, this is also helpful so they can keep an eye on any unruly children during the meal. ("Johnny, quit kicking your sister under the table." "Susan, eat your peas, don't hide them under the mashed potatoes.")
On a cruise ship, it is considered to be invited to sit at the captain's table. The captain, of course, would sit at the head of the table. In your example, the guests had two esteemed members of the crew at their table - the chief engineer sat at the foot of the table. Normally, the captain would be at the top of the hierarchy, but apparently in your scenario the two men treated one another as equals. However, it's impossible to tell the exact meaning without seeing the rest of the sentence ("they sat with equality....") It could mean that they treated the passengers as equals.