How is this achieved?

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It's simple really. Most of the terrains in the gallery are Blitz terrains with one big texture stretched over them. Even my own terrain system uses rather large areas that have a single texture, to make it easy for the user.

But these screenshots are using custom meshes, with tiled textures.

Look at where the lightest green grass goes into the darker and then the darkest. See the line? Really sharp. That's because that is actually the edges of polygons.

To do this in Blitz, you'll need three seperate grass textures, probably 512x512 for the crosshatch one, but you can use smaller ones that tile more for the others. Plus a smooth sand texture, and a gravely sand texture.

Make one surface for each texture in your mesh, and then model each region for each texture. So your sand trap would be a smooth oval.

It would probably be easiest to do this as follows. Make a large grid to represent the whole course. Deform it with your heightmap. Then create spline curves over this which represent the various regions of texture. Then cut the grid with each of these splines to create seperate regions with smooth borders. Finally, seperate the regions into individual objects, and apply a repeating seamless texture to each so that the texture looks nice and detailed.

And that's it. These courses don't even seem to have lightmapping just vertex lighting, so you're all set there, though I do see a tree casting a shadow. My shadow system could do that for you.