I was about to say "Clues appreciated" but you have edited the post while I tested.
I just generated the sample project Employee Care 3 using both 2015 and 2017.
In 2015 responsive help (Azure Blue layout), the help starts to open in Edge but fails to load the TOC or default topic.
WebHelp opened OK and at a quick glance the only issue was the index not showing.and that was the same in Firefox.
In 2017 both were OK.
Try Support as the responsive issue was in 2017 but fixed with an update. Maybe they have an updated layout for 2015. Please post back with their response.
See www.grainge.org for RoboHelp and Authoring information
I have reported this to Support. They will investigate and let me know a solution or what they find by the end of play today (apparently)!
Well, Support never came back to me with an answer or resolution when they said they would. Thanks 'Apurva' on support. Great service.
There is a solution to this. Click this link Support provided. I have downloaded a replacement file and installed and re generated help. I can confirm Responsive Layout in RH2015 using ME Edge now works correctly.
Hope this helps.