Welcome to the forum!
Never heard of Mermaid editor. As far as I can tell, the live part is where you enter code in a box and it produces, afaict, flowcharts and diagrams, and such? That doesn't look like SVG code, in the box. But I guess you click the button when you're finished, and it produces SVG code?
I found the Mermaid github account, but... Oh, I see, it says the code that you input is javascript, and then it outputs SVG.
Can't seem to retrieve the SVG code, from the link you provided. I click the download button, but nothing happens. Is the SVG file that you attached the code created by mermaid?
I'm far from an expert in SVG/XML. But my best guess is the arrowhead which was created in mermaid, does not exist in Inkscape (so it can't display). Try opening a new blank document in Inkscape, draw a line and apply one of the stock arrowheads. Then you can compare the codes.
I wonder if the quotes being present in the mermaid code might be part of the problem, since I don't see quotes in the Inkscape-made arrow. But as I said, I'm far from an expert.
Someone else with more helpful information should be along before too long