The answer to this question can get a little complicated, depending on how accurate you want to be.
Regardless of bar position, the centre of mass of the bar is always half way between the landmine attachment and your grip, meaning that its weight is divided evenly between the two. So if you want to know how much to add to the plates on the bar to get the total weight, 10kg would be a reasonable initial approximation.
Caveat: In a landmine squat, you have some leverage due to the fact that you're gripping the bar further away from the point of rotation than the plates, which means that the landmine itself will take about 10-15% of the weight of the plates on the bar, leaving you with 85-90% of the weight of the plates, plus 50% . So if you have a 20kg plate and a 20kg bar, the total weight would actually be 10kg from the bar, and maybe only 18kg from the plate, adding up to 28kg.
Now, I should also mention the angle of the bar, since that's been factored in in another answer. I don't think the bar angle alone affects the load placed on the lifter, but rather the combination of the bar angle and the angle of the lifter's body (measured between the centre of their feet and the point where they're holding the bar) does. The body angle doesn't change as much as the bar angle does, since the lifter's feet are fixed in position, which results in the lifter never really pushing at 90° to the bar, and instead leaning more into the bar at the top of the lift. The effective load decreases as the bar angle increases (becomes more upright) and increases as the angle at which the lifter pushes on the bar moved away from perpendicular. I estimate that this will mean the lifter needs to exert force equivalent to 82% of the previously calculated weight at the top of the lift, and 95% of the previously calculated weight at the bottom of the lift. If desired, I can add in my calculations, but I really think they're unnecessarily complicated as an answer to this question, and I'd recommend just ignoring the angles of the bar and lifter.
As an aside, I think the linked article vastly overstates the benefit of landmine squats, and unfairly criticises back squats. I can't think of a single situation in which I'd recommend a landmine squat over any kind of free-weight squat.