Rainhandler.

Right, but assuming we installed a gutter in that area shouldn’t that act as the rain handler?

No, that's not necessary. I used to live in a forest house, way back when, that had no gutters due to having a 500 year old oak grove around it. The edges didn't have said gravel drips, just the forest soil. And we didn't get gouges, creeks, or whatnot.

But I think the designer did a pretty good job there and the roof was never very long or large at any one point.

I would think, for a roof that short in length, you could simply let the grass grow back to the edge, or install a garden of sturdy stuff that won't mind the occasional minor waterfall, and it should do fine.

My house in San Antonio had the soil wash out under the drip. Nothing grew there. We installed a Rainhandler on one side and used mulch elsewhere.

If there is a gutter or a Rainhandler (which I personally LOVE), then you could grow grass up to the foundation.

You don't technically need the gravel strip if you have gutters and downspouts. Your house could use planting along the foundation, but it would occupy most of the grass and walk space shown, so you might not be able to have it. The ornamental grass such as what's in the container is not going to fit in the skinny space now occupied by gravel.