Does not look like real leather. If it is real leather use saddle soap to clean then dubbin to seal and soften the dubbin. That is what I use on my boots and they get real dirty
It's hard to tell if that is surface dirt, mold or if the surface of the vinyl has been worn off. I would try a Majic Eraser on a small area but keep in mind its abrasive and will remove some of the vinyl/
Vinyl has a shine surface. You have probably worn it off thus the stain. You can try 10% bleach in a very small area then wash well with mild car clean soap. Do not use dish detergent. Once you got it clean you need to seal the material. A car shop can advise on the best product to use.
Before you go to magic eraser, Use a degreaser. Something like Meguiars super degreaser. And a series of scrub brushes. You can search you tube. Some the auto detailers swear by it.
In this order: ivory soap with microfiber white cloth; if still there, 409 with micro fiber cloth; if still there, gentle rubbing with micro fiber cloth and Soft'nScrub with bleach; if still there, Magic Eraser. Once it is gone (and it will be), wipe it all down with a wet micro fiber white cloth and dry it. When it is clean, give it a good treatment of 303 Protective spray and buff.
severe to bad you use chlorine diluted with water and wipe on wipe off... its the only thing that will remove deep mildew that has stained the vinyl..
eventually you are looking at replacement..