DIY

Looking at the images you've attached, this appears to be an 8 ft wide by 6 ft tall fence. That's a good amount of weight in just the wood, and there isn't any part of the design that diagonally braces the frame, except the steel cable... which tore from its mounts.

My layman's view is that you absolutely need diagonal wood elements, which should only be installed after unloading the fence, either by removing the boards or by propping up the wheel-end so the frame returns to being squared. If the wheel interferes with this, remove it for the time being.

But I think you'd still need the steel cable, and if that has broken from its originally designed mooring, then this gate is already compromised. You may have to start over with a new Adjust-A-Gate kit or repair the current one so the cable will mount to the steel parts, rather than the wood.

I would say to rectify the diagonal supports first, before doing anything with the hinges, since if the hinges were actually the root problem, this gate would have already fallen over. That said, it seems to me that such a wide gate might have called for more substantial hinges.

The other commenter's suggestion to consider a pair of less-wide gates is also sound, if the goal is a minimal-fuss gate that will last at least a decade of additional sagging and weather.