Does three dots in linear make sense "more" in web applications, i have seen them only in mobile design?
Most of the user would not know what ... means. Try this
They almost make as much sense as the word "more" ...
As with any icon, I personally have taken to do what you're doing everywhere else in that design: use an icon with a word next to it.
Or "Menu" followed by the hamburger icon.
Alternatively, use a down arrow. That one has worked for years, and is still seeing heavy use across (web based) applications.
Why don't you use a small drop-down arrow here? This icon is ok, but seems that some dialog box/window will be opened by clicking this. Yes you are right, this icon is used to display More options.
Dots, in this form, are communicative of either loading, or progression. As suggested above, a drop arrow would work well. Perhaps, consider an angled arrow as this also hints at the path new content will appear in.