If you downscale the image outside the game then the game is going to have to upscale it itself to display it, so the end result will entirely depend on which upscale filter the game is using.
For that generic resizing software, you probably got artifacts because for a texture, it's gotta join on the edges, but the software doesn't know that, so it's not correctly oversampling across the edges.
When you downscale, you need to sample a region of the texture, and generate an average color. For a texture that has wrap-around, you'd need to sample across the edges. One way to trick it into working would be to make a slightly bigger image, with parts of the edges added on. Then, you downscale that, and then crop back out the unneeded parts. That way, the image would have the correct sampling across the edges.