Sorry, but I don't see anything wrong in the photo. Everything looks fine to me. Why a gutter? A terrace always has a slight slope away from the house. This is what a professionally flawless terrace by the garden landscaper looks like here. Under the stones at the house and in front of the plant pots are drainage pipes, terrace with slope, a step with a small threshold towards the door, water will certainly never get into the house. Karsten
You have a step and – I can't see clearly – probably a normal patio door with a frame at the bottom, right? Usually, no gutter is required there. For threshold-free doors combined with directly adjacent flooring, a drainage gutter in addition to the slope is state of the art (whether there is a DIN standard for this, I don't know). I would always install the gutter if I don't have an extra step in front of the door, regardless of whether it's threshold-free or with a simple threshold.