I have not grown horseradish, but my grandmother did. She just grew it in the ground, though. Many people actually recommend that this herb be grown in containers, because it can be quite invasive. In a container, tap roots just grow around and around the inside walls of the pot. Many plants that have tap roots are successfully grown in containers.
One thing I would like to point out in the article you linked is the comment
The plants were old, formed large clumps, and had grown undisturbed at least 10 years.
I hope you don't intend to leave your horseradish plant in its container for 10 years. One hopes you will dig up the roots and use them when the plant is 1 year old. I understand that's when they have the best flavor. Container grown horseradish must be replanted every year.
If I were going to grow horseradish, I would use a half-barrel. I would plant the roots in early spring or late fall. My grandmother always laid the roots at an angle in the planting holes, with the narrow ends about half a foot deep and the tops just peeking out of the soil. I see no reason why that same technique shouldn't work in a large container.
I don't remember my grandmother using fertilizers, but she always used various manures which were available from our family farm. (We didn't live on the farm, her brothers ran it.) I would use a potting mix very rich in compost, probably a commercial mix, to ensure excellent drainage, and to that I would add additional compost. A combination of 2/3 potting mix and 1/3 compost might be about right, but you might want to experiment a bit. You don't
want to give horseradish -- or any root crop, for that matter -- a high nitrogen fertilizer, because all you'll get is nice greens. You want to encourage root development.
Beyond that, I would treat it like any other container-grown plant, keeping it evenly moist, but not soggy, etc. I would give it full sun. If you plant a root that has leaves, keep it out of the sun for the first few weeks. Be prepared for the top growth to wilt. The leaves won't perk up until the root becomes established enough to provide them with moisture. During this time, keep the soil moist, but be very
careful about overwatering, because the roots won't be able to pull moisture from the soil. Once the top growth perks up, you can be a bit more generous with the water.
I hope this is helpful to you. I'd be very interested to hear if you succeed or not. I love horseradish, but like so many other food plants, I don't grow it because so much would just go to waste.