Yes and no - Quicktime is the default player for MOV files and both were developed by Apple.
. . . . .mov an outdated file as compared to the new players like mpeg4 and H264 . . . .
Again the answer is yes and no -
Yes - MOV is an old format.
No - because it is a container file and not a specific video format like h.264. Being a container file format it can contain virtually any codecs such as h.264 and various audio codecs inside it.
As you can see MOV is definitely not an out of date file format because it is adaptable, all it needs is Quicktime installing to be able to use the encoders and decoders to create / play the MOV file.