I played a lot of the original Civ but it was in the early 90's so my memories are a little hazy now. Units on the world map had a "zone of control", you couldn't move units through tiles adjacent to an enemy unit, so the behavior you mention where you could juke past a stack of units wasn't possible, you could put units around cities and similar to create blockades, cut off reinforcements etc (including with naval units).
There was even a tile improvement you could build "fortress" which was useful to build in chokepoint areas as it gave defenders a big advantage. It made this blockading tactic more effective.
The big difference I feel going from old school civ games vs newer games is map tile improvements in old games you had to dedicate a unit to upgrading the tiles around cities (you would have units dedicated to permanently building irrigation, mines, roads and in late game they'd be on pollution cleanup duty to avoid global warming occurring). In modern civ they've abandoned this.
Alpha Centauri was the peak civ game for me had so many cool things you could do like nerve stapling (removed the cities unhappy population permanently but also removed specialists), population booms - where you could grow cities extremely fast by funneling a massive amount of growth resources into them, Supply crawlers (could ferry resources from any tile on the map to crawlers home city), multi tiered social civics (for example rather than just playing a constitutional republic, you could be a combination of Democratic/Planned Economy or Fundamentalist + Free Market, Police State + Green Economy etc.)