Are there ways in which God is like us?
Yes. God loves, hates, plans, creates, thinks, builds, achieves, expresses Himself, takes pleasure in beauty and diversity, is disgusted by cruelty and evil.
God communicates.
God enters into relationships. (Source: Pastor Steve's Beliefs)

In a sense, the author is correct. God, according to the Bible, is and does all of those things. But I think the author is a bit sloppy: He has the direction backwards.

No, God is not like us. We are like God. Not in the New Age sense of being gods or even "god-like", but instead being made in God's image so we reflect a portion (albeit sometimes a tiny portion) of His glory. If we were to say that God is like us, we would be anthropomorphizing God, making Him like us. We should try to think in the right direction (top-down rather than bottom-up) regarding God.

For example, when we refer to God as "Father" we have a tenancy to apply our conceptions of our own father to God … which of course is quite backwards. To use Platonic terms (hopefully correctly) God is the Form, and our fathers are the forms. Or to put it another way, God is the mold, and our own fathers (as wonderful or as miserable as they may be) are the clay, which imperfectly represent facets of the original.

Of course, such similarities of God are marred (but not erased) by sin, which causes us to feel separated but not entirely estranged from our heavenly Father.

Related: How does sin estrange us from God? And what is God's answer to the problem?