I just fixed that paragraph. It will hopefully avoid some confusion.
By the way, x264 isn't really a codec, it is just an encoder. I'm also not sure calling H.264 a video format is really correct, it's more like a codec standard to me. But I guess all of this is just wording bikeshed :)
It's a very easy subject to confuse, thanks for making a correction.
H.264 is literally a document, describing a bitstream that represents a video. Calling H.264 a 'codec standard' is correct in the same way that calling ISO C89 a 'compiler standard' is correct; there are several things you can do to C code without compiling it (for instance, intelligent preprocessing, interpreting, static analysis..). In the same way, there are things you can do to an H.264 standard video without encoding or decoding it (remux, retime, cut, join, ...)
I don't seriously intend you to take this remaining sentence to heart, but to play the pedantry; libx264 is the encoder. x264 generally refers to the command-line client, which happens to contain several decoders - a trivial native YUV decoder, but since about r1400, it's often statically built with all of ffmpeg/libavcodec's decoders, which makes ./x264 or x264.exe a de-facto H.264 decoder (even if it can only output H.264 again)
