This is a very simple thing to diagnose and to correct.
" The fly line is going to travel in the direction the rod tip travels at the end of the stroke."
Your rod tip is traveling from right to left at the end of the stroke, and so the fly line must follow it. You are making what is commonly referred to as a, " Curve cast."
The fix is to ensure that the rod tip travels straight at the end of the stroke.
The same is also true of the line splashing in the water at the end of the cast. Simply aim the cast higher.
You can prove this to yourself quite easily, in the abscence of wind:
With about 25' of line out of the rod tip, make an overhead cast and at the very end of the stroke, flick the rod tip from left to right. See what happens when the fly line lands on the water?
Best of luck with it!