At present (180818), it is is only possible to measure either
1\. the length of a single track segment or\,
2\. the sum of the lengths of all track segments in a multi segment track\,
irrespective of whether the overall track is a single continuous trace or is a set of branching segments connecting multiple nodes (pads or vias).
It is not possible to measure the length of a set of contiguous track segments between an arbitrary pair of nodes.
The series of screenshots below illustrates the problem.
Click on a single net segment:

The length of that single segment is shown.
Click on a net segment and then press "H" to highlight the whole track:

The whole net is highlighted and what looks like the total length of all segments is shown.
Click on a net segment and then CTRL+click on another contiguous segment to highlight a branch between two nodes:

No length is shown.
Now go to the Design Manager and click on the net:

The whole net is highlighted and what looks like the total length of all segments is shown again.
Chrome
68.0.3440.75
Ubuntu
EasyEDA
5.7.19