You are correct that Mission Control mainframes sent data to the command and lunar modules.
The problem (imho a fatal flaw) is that the computers on board the modules had no on-board real time navigation computation capability—which would have been needed to safely land the craft and then return the lunar module to the command module at a later point. The real time would have been necessary because of the communications time lag between NASA and the capsules when they got near the Moon.
The computers shown in official NASA documentation were “Potemkins”—fakes.
That is what the links show—and is one reason many of us believe the missions never happened—despite all the name calling and insults we get around here.
There was a lot in the book I mentioned about how the astronauts made a LOT of manual calculations, and the on-board computers could be rudimentally programmed or used manually as interfaces. I used to be able to do that when I was a young engineer, a lot better than I can now. I know guys who can still do complicated calculations as naturally as they breathe.
And these guys were engineers and pilots - that’s what those guys do. The plans were in place ahead of time to begin orbits and ascents/descents in certain windows. The “rough” part of the calculations were done way ahead. You don’t risk doing that real time if you don’t have the computational power. The real time stuff was controlling the attitude control engines by hand after you got close. OR by referencing tables and plugging values into the proper calculations, quickly. Again - pilots - it’s what they do.
There was a whole section of the book that talked about how these guys had to learn that orbiting was not like flying. Thrusting forward makes you lose ground on an orbiting target, and backward thrusting makes you catch up. Simple, but foreign at the time. Everyone knew they better have their ducks in a row before they got there, especially for the close maneuvering. It was a whole new framework that they studied to death because it was actually life or death.