It's a beautiful jacket and looks like a gorgeous and unusual neutral color. The sleeves look long, but not not too long in my opinion. The jacket fits you so well, it just looks like the sleeves are supposed to be long, like they are meant to be long enough for the jacket to be worn as outerwear if desired. Personally I like the look of them zipped, which you've noted that you don't like.
I am not an alterations expert, but I sew, and I think shortening the sleeves could be tricky, but not impossible. You can shorten a zipper by cutting it off, so theoretically the sleeves could be shortened. I'd ask a tailor how much it would be and weigh the cost with that of finding and buying a different jacket. It might be well worth it.
ETA: Another, easier way to shorten the sleeves is to take up the extra length above the top of the zipper--i.e., somewhere around the elbow. That would change the look of the sleeve substantially, adding a seam around its circumference of the sleeve, which you might or might not like. But it could be made to look consistent with the jacket design, with topstitching added to match what's done on the rest of the jacket. And it's not that unusual to see extra seams designed into leather clothing.
