The biggest problem I have with this style is that it is inconsistent across variable types and provides no insight into the actual operation being performed without further knowledge. My personal experience is that my ability to read and comprehend code quickly is dependent on the context and patterns present within it (among other things). Therefore making the expression explicit as a pattern adds context and therefore increases readability and comprehension.
The statement '!x' tells me nothing about x, just that I'm expecting a given logical value. The semantic meaning of that value however, I have no idea. Odds are it is probably a NULL or 0, but that doesn't help much because (at least in the linux world) they can have different meanings despite having the same logical value. I cannot differentiate between success (!(x == NULL)) or failure (!(x == 0)) without more context.
The statement 'x == NULL' immediately tells me at a glance that I am dealing with a pointer, and therefore I should pay more attention to how it is used. I know I should now be looking for other patterns of safe/unsafe pointer management that are immediately relevant to the function I am reading right now. There is no need for me to look elsewhere and go on some tangent to find out, then to have to recall what I was doing when I come back later. I can immediately start considering the likelihood of segmentation faults, or other memory management issues. x == NULL also tells me that here I am expecting failure of some kind. The context around that condition should then tell me which kind, eg NULL == alloc_thing() vs NULL == find_thing().
Similarly, the statement 'x == -1' tells me I am working with an integer. This can tell me immediately whether I am expecting success (x == 0), failure (x == -1), or that I should make a mental note of more complex possibilities (THING_WORKED == do_thing()).
Code is a narrative. It is documenting the answers to the questions you are asking while writing it, and it should answer the questions that someone else is asking while reading it. When somebody asks you to explain something, the least helpful thing you can do is answer a plain "yes" or "no". It is better to give context and answer further related questions before they need to be asked. Readability and comprehension of code are no different - any given programmer is asking questions of the code. The more questions they have to ask, the longer it will take them to discover the answers in order to understand the code. Context helps. Shorter is not always better.