Would not recommend. If you’re laying over concrete, maybe. If you’re laying over tamped stone, no way, no how. The stone dust will shift under them over time and cause you far more headaches than the few extra bucks proper rubber mats would cause. Add liquid (from power washing the barn, horses peeing in the aisle, water bucket spills or auto waterer malfunction, etc.) and that shifting is going to cause you massive headaches.
I did a lot of research before purchasing and installing for a client’s event inside a large tent over well tamped, levelled stonedust. While the stupid things held up well to several thousand people walking through and they were cleaned up and taken home by the client for use in a garage, they were a GIANT PITA to install and there was some shifting over the 3 days which included popped seams which could not be put back together without ripping out a huge section. The next year we did indoor/outdoor carpet and while nobody was fond of sweeping it every 5 minutes, it was much less trouble than the tiles.
I also worked in the parlour of a dairy farm with similar (thicker and tougher) plastic tiles for several years. They were beautifully laid over concrete. They had to be taken up once or twice a year for cleaning because stuff gets through the cracks and festers
under there. They also got terribly slippery if anything even slightly greasy got on them. Add water and you WERE going on your ass, no question. Not an issue when you’re cleaning the joint with a scalding hot pressure washer 3x a day, not practical in a horse barn imo.
All that to say, you’re probably going to be ripping them out and reinstalling them more than you’d like no matter what base they’re going over.