DBSCAN is a 'density-first' (my own words) algorithm, meaning that it requires a base density of minpoints (but including itself) within eps distance of each other to declare a cluster of core points - and only then border points may be added to existing clusters, if their distance is within eps of core points.
In your example, there is no point that has 3 nearest neighbors within eps distance, which would be required to form an initial cluster. Simple as that.