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I know this is obviously not true for some games, minesweeper, card games, etc. But what about any game involving simulating the real world environment. Obviously these games have some form of a physics engineer powering the graphics.
For someone like me who personally did not enjoy physics but loves video games, do I have a chance at ever getting involved in the development cycle of a video game such as this while disliking physics?
There are many aspects to game programing and you don't need to be an expert at all of them. If you're on a bigger team you may not even be doing the core game programming but just network communication for example.
For core game programming I would think that above a sound physics understanding you would need a strong mathematical background. Having a strong mathematical background will allow you to do things like modelling transformations, clippings, keyframe animation, ray tracing, image processing, texture mapping, etc.
Having a strong physics background may help you with coming up with new computer graphics methods, but it is not required if you want to become a game programmer.
It's very rare to write a physics engine for a game anymore. Usually, a third party library, either free or commercial, is used instead. The same goes for other aspects of game engines, too. Rendering, sound, AI, animation, GUI, networking, etc. It's rare that anyone writes a game engine from scratch these days. Usually people buy them. If they do make them, they buy a bunch of middleware to do the difficult tasks.
There's lots of places to start learning game programming. If you want to just go "make a game" I'd suggest diving into Unity. Unity is a fantastic, very easy to use game engine that can be used to make just about anything. It even provides most of the features of commercial engines (especially the upcoming version 3).
If you want to learn more about the fundamentals of game programming, check out PyGame or XNA. They take away a lot of the tedium normally found in managing graphics, input, sound etc. They won't do physics for you (they are not engines, just APIs), but there's a lot of free, easy to use solutions.
