Understanding the equations and implementing them, and even understanding that integration is what you need are the parts that math helps you with
The point is that you don't have to understand them to implement them. You actually need to know very little. Yes, it's helpful, but it's far from essential. That's the point. No one is arguing that you're better-off knowing nothing about math or physics, only that it's not that important for developers even when it superficially appears that that understanding is necessary.
Now we're having a completely different discussion...
How do you make characters move intuitively? By making them inhabit a world that follows physical laws similar to our own.
If I remember correctly, in Super Mario you could move left and right while in the air. That is pretty obviously outside the physical laws of our universe. They did this to give the player more control over their jumps. It feels intuitive, even though it's completely different from the laws of the universe we inhabit.
How do you make sure that a character follows a realistic, predictable, intuitive parabola through the air when they jump?
By abandoning Newton and developing a system that works well for the game. Give it a try. Write a simple side-scroller that accurately reflects the physics of the natural world. You'll be amazed at how terrible it plays. I did a quick search, and found a number of discussions that seem to support this. I also found a few breakdowns that may interest you: Sonic Physics, Super Mario Galaxy Demystified, Mario Gravity, SMB Physics.
That second link has a nice quote: "Obviously, real world physics have a place in today's games. However, they take a backseat to psychology when it comes to making real world gameplay"
Perhaps we can put this issue to rest.