The basics
Neither the plugin's documentation nor the QGIS native tool Points along geomtry (which I would recomend) does mention any possibility to change between cartesian and ellipsoidal distances. Why that is should become clear in what follows. Ellipsoidal distances follow great circles:
The minor arc of a great circle between two points is the shortest
surface-path between them. In this sense, the minor arc is analogous
to “straight lines” in Euclidean geometry.
From Wikipedia: Great Circle
See also: Wikipedia: Great Circle Distance, Great Cirlce Navigation and Geodesic.
So for what you want to do, some basic knowledge about projections is necessary.
The solution
To achieve your goal, create a custom oblique azimuthal equidistant projection. This projection returns "true" (ellipsoidal) distances from one point (the center of the projection) to all other points on the map. This is easy to do using Projectionwizard.
For background about this projection see ESRI: Azimuthal equidistant and Wikipedia: Azimuthal equidistant projection
Step by step workflow
Get the lat/lon coordinates of the point from where you want to start measurement (the line's start point).
Go to https://projectionwizard.org, click equidistant projection, below enter roughly the coordinates of your start point and when done, click WKT and then copy the WKT definition (see screenshot and projection defintion in WKT format at the bottom).
In QGIS, go to Menu Settings > Custom Projections..., click the green + to add a custom projection, enter a name and paste the WKT definition from above. Change the values for Central_Meridian and Latitude_Of_Origin to the exact lon/lat values you want (see step 1). Cf. screenshot at the bottom.
Reproject your line (e.g. using save/export) and use the custom CRS created before.
Use the resulting line with Menu Processing > Toolbar > Points along geometry and set the distance you want.
Explanations
The result looks like this: black = initial line, blue = points along the line: exactly 200 km away from each other. You will object "but they do not lie on the line" - well, this is not true as I will explain below:
The map canvas above is in project CRS EPSG:3857, thus in a (Mercator) projection that heavily distorts distances the further you get from the equator: north of Greenland (as in my screenshot), distortion is extreme. So the black line you see connects start- and end-point of the line in this distorted projection.
The "real" line - the shortest connection between start- and end-point on Earth's surface - follows the shape of the red line (you get this red line using Menu processing > Toolbar > Densify by interval).
You see that if you change the project CRS to the custom projection from step 2/3 as in the following image. The black line now follows exactly the blue points, where the red line here represents a line drawn in EPSG:3857. The point at the bottom left (red arrow) is the center of the projection: all measurements starting with this point return correct (ellipsoidal) values:
That this is indeed the "true" shortest path connecting start- and end-point on Earth's surface can be seen on a globe, e.g. if you export the line and open it in Google Earth. As you can see, the direct path does not intersect with northern Greenland:
Step 2: projectionwizard
Step 3: Creating custom projection - paste WKT definition
This is how the WKT definition looks like for the point I used (76° N 82° W)
PROJCS["ProjWiz_Custom_Azimuthal_Equidistant",
GEOGCS["GCS_WGS_1984",
DATUM["D_WGS_1984",
SPHEROID["WGS_1984",6378137.0,298.257223563]],
PRIMEM["Greenwich",0.0],
UNIT["Degree",0.0174532925199433]],
PROJECTION["Azimuthal_Equidistant"],
PARAMETER["False_Easting",0.0],
PARAMETER["False_Northing",0.0],
PARAMETER["Central_Meridian",-76],
PARAMETER["Latitude_Of_Origin",82],
UNIT["Meter",1.0]]
