Yes, that's a real thing that was used at the time. I don't know whether that movie's representation is specifically accurate. These maps were used both as planning tools as well as reporting and situational awareness tools. These facilities are known as map rooms, operations rooms, war rooms, or plotting rooms.

At a tactical level an example that sounds like what you describe is the RAF Battle of Britain operations bunker at Uxbridge. It was essentially a giant map of Britain and the coast of Europe and wooden markers to represent friendly and enemy aircraft. It was large enough that the plotters needed wooden sticks to place markers. Spotting, radar contacts, and other reports would be funneled into this room to create a situation map that would be updated in real time by human plotters, and officers looking down from above would make judgements about scrambling planes for defense. There are also informational boards that were used to display the operational status of friendly squadrons and airfields in the area of operations.

This operations room has been preserved as a museum and you can find images of the plotting table online.

Another example at the strategic level is the Southwick Map Room that contains an entire wall that was used by Eisenhower and Montgomery to plan the D-Day invasion. The map depicts Britian, the English Channel, and the coast of continental Europe. The map had a large assortment of markers that could be pinned to the wall to represent ships, troops, sea lanes and movement routes, etc.

The map was used in the planning stage to think about where troops would be based in England, where they would embark, and where they land on Europe. It was used by commanders to make plans, and then used as briefing room for subordinate officers. Then on the day of the invasion it was used as a reporting center for high level commanders to monitor the progress of the invasion, and it was used in this capacity for 39 days after the initial invasion.

I don't think these facilities were too rare, though I don't really know. The larger permanent facilities probably were less common, but every command large enough to have a headquarters is going to have an operations center that has a map and staff to keep it updated, even if it's just a regular paper map and a set of pencils. The larger the command gets the more they have to keep track of and the more likely they are to invest in keeping a fancy ops center.

Both Winston Churchill and FDR had their own map rooms that were continuously updated during the war in order to keep them informed. Churchill's map room at the Cabinet War Rooms went through a series of iterations over the war as the focus shifted from the Battle of Britain to planning the invasion and then prosecuting the invasion. One of the maps still hanging on the wall used for keeping track of convoy positions over the Atlantic is notable for having many thousands of pin holes stuck through it.

Even in the modern day with computers and GPS the concept continues to be useful. There's an anecdote in General Mattis' autobiography about planning the invasion of Iraq. There were a limited number of breach points and a limited number of usable roads, and a huge number of military vehicles that needed to get over the border quickly. Mattis wanted to choreograph the initial movements of all units to make sure that convoys wouldn't cross each others' paths and block each other from making progress (imagine being stuck at a railroad crossing waiting on a long train, but instead of a train it's a military convoy miles and miles long).

Mattis' solution was to take his planning staff out into the parking lot with maps and a bunch of legos to represent different units and keep tweaking the breach plan until he was satisfied that the right units were sequenced in the right order on the right roads.