A map without tiles would need some other geometry to define movement and placement of Improvements, Cities, armies, etc on the map.
The new game ARA appears to do it with Regions and Sub-Regions, but these are, basically, just Larger Tiles each of which potentially holds more Things. And larger tiles, of course, simply makes the map effectively Smaller because there are fewer options available for movement and possibly for placement.
Another way is to use Nodes and fixed lines of movement. The old board game Soldier Kings used this geometry, ion which each Node was a city or town and the roads between them were the only way you could move, and all movement was from Node to Node. This works very well when you are modeling a simplified situation, as that game did for the wars of western Europe in the mid-18th century, but it is far more problematic if the essence of the game is building an Empire and founding cities and therefore constantly changing the Nodes and methods of traversing the space between them.
One 'semi-tileless' method is to use tiles much smaller than the items displayed, so that placement and movement options are vastly increased. It's as if each tile in Civ VI became 10 tiles with all the 'extra' options for movement and placement within them. The obvious problem is that on Civ-sized maps it would make it impossible to tell what was in a tile without zooming in on it, so that the game would become a constant series of zoom in/zoom out actions until you became violently nauseated from vertigo.
I'm sure there are a host of other options, but those occured to me right away and, frankly, none of them appeal very much as any improvement over what we have now for ease of play and certainty of placement and space to place and maneuver game elements on the map.
