After searching comments on youtube for hours I found a few people having same issue, OPTIMAL DISPLAY on SUBSURF MODIF should be UNTICKED , and Xray dropdown under Geometry WIREFRAME should be set to 0.5 to get the same display as Andrew.
Once you've switched to Wireframe mode you can disable the X-Ray mode, and you can select your object and in the Properties panel > Object Data > Viewport Display > Display As > Wire. This way, only this object is transparent.
(presumably also valid for 2.8 versions)
Use Skin Modifier
A simple way is to convert the mesh into curves, then bevel it, what gives the resulting "wire" a solid appearance. In Object mode:
select object and in top menu go to Object > Convert to > Curve
in the Properties Tab under Curve ...