Orthogonal projection of 2D map.
The sprites you have probably assumed the game would 'flip' the sprites horizontally at runtime. Left is can be seen as the same as right, just mirror image opposites. Another option is to flip the sprites in an image editor. Even MS Paint has a flip option.
As for tiles that are similar to what you're looking for, are any of the ones here good? http://hasgraphics.com/category/tilesets/
I tried flipping the image with GIMP and pasting the flipped images on to the sprite sheet. But something is wrong. When the object moves right, the movement is jerky. When it moves left, it's smooth.
Are you sure it is an exact mirror of the original? If you don't align the images in the spritesheet an exact distance (usually) then the actual texture will be slightly bigger than the sum of all the animation frames, meaning the frame width/height will be calculated incorrectly
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