... On Open street map there is a connecting path and something of a dirt road going to this trail, allowing to make sort of a triangular walk from Agios Ioannis. I can't make these paths out on the satellite images, do they actually exist?
From Kakos Poros a trail towards Selouda does exist as shown on the OpenStreetMap image above. The beginning of the trail (at Kakos Poros) is actually marked but only for a few meters. Then it becomes more or less invisible due to a thick layer of pine needles.
The walk is very easy and as far as I remember it takes about 35 minutes to walk from Kakos Poros to where the trail meets the Agios Ioannis – Selouda path. But the trail leads through dense pine forest and since you only once or twice get a glimpse of the sea far below or of the edge of the cliff you'll need to have the trail on a gps or you'll loose your way within seconds after having left Kakos Poros.
You can create a route on an OpenStreetMap installed in e.g. Garmin's Base Camp application and then export it as a gpx-file to a gps. In other words; a triangular walk Agios Ioannis – Kakos Poros – Selouda – Agios Ioannis is possible.
I have no info about the red dotted "shortcut" on the OSM image.