The path to the hut is for mountaineers or people with knowledge of alpine terrain. This is indicated on a sign in the lower part of the path. This does not mean the entire path to the Domhütte, but only the section from the Europaweg to the Domhütte. My comments only refer to this section. The rest of the path can be hiked normally, provided you are in good shape.
Sure-footedness is highly recommended. The path there requires a lot of fitness. It also contains several climbing sections, some of which are equipped with safety chains or steel cables in places. There are also some footholds. Nevertheless, the path is not without danger.
Rope and climbing harness are not required for the climb to the hut. Gloves (possibly fingerless gloves) prevent your hands from slipping on the steel cable and could therefore be useful. Walking sticks can make the climb easier in places, but can be a hindrance on the climbing sections on the descent. Sandals or light sneakers have no place there. Mountain boots are more the norm here.