in this particular case, the map appears to be one big bitmap made in a paint program, not tile based.
odds are there is an underlying 2d array map (not displayed) that units use to determine what terrain they're on.
or it may be a bitmap and run at pixel resolution.
either way, the idea is the same. you have a 2d array of bytes or whatever, indicating wood, grass, water, wall, etc. this is how you tell what terrain and obstacles are where. the map on the screen is a pretty picture that matches the underlying "game map". the resolution at which units move may give you a clue as to the resolution of the underlying game map used.
the grey grid lines are just drawn over the pretty picture as extra chrome. the net result is a beautiful battle map on the screen that matches the simpler underlying 2d array map actually used by the game logic.
for this approach you'll be looking at some quality time with your favorite paint program.