Can genetically engineering the DNA of a human zygote, make it a twin of another human in entirety?
The answer is no, and it is because sequence of the genome is not all information that is required for gene expression and development, there are also epigenetic factors. 

A lot of patterns of epigenetic marks, such as most of DNA methylation and some histone modification patterns, are set during parental germline development, and these marks are transmitted to the zygote by gamets (except paternal histones, those are not transmitted because they are temporarily substituted for protamines in sperm for greater compaction). Therefore, the naked DNA inserted into zygotic nucleus will not have access to the machinery that established epigenome during development of the gametes. 

And even though nucleosomes may assemble in the zygote on the naked DNA and histones may acquire post-translational modifications, and cytosines may get methylated, but most definitely the zygote is going to have no means to correctly set distinct patterns of epigenetic marks at alleles that are normally imprinted, i.e. those alleles whose epigenetic state depends on the gender of the organism that produced the gamete.

Therefore, the twin created in this way will have the same DNA sequence, but it will be a  subject to disorders associated with imprinting