Here's a few reasons why God alone is worthy of worship:
As Christians, we worship God, because his creating, sustaining, and redeeming acts are quite literally the highest gifts that we could possibly receive; and worship (expressed in both obedience and song) is one of the rehumanizing ways that we express our delight in God and the good gifts that he's given.
With this in mind, if the God of the Word is who he says he is, then when someone adamantly refuses to worship God, what they're really announcing to God and the world is: "Although you've given me the highest gifts that I could possibly be given, I have no obligation to glorify, thank, or worship you for what you've given me (see Romans 1, esp. vv. 21-23)."
This refusal to worship God, because of the gravity of the gifts that he's been given is no small refusal, because if we have no obligation to honor the One who's given us the highest gifts, then why in the world should we be obligated to honor those who've given us lesser gifts?
If a person thinks that the refusal to worship is a small and insignificant oversight (a variety of stubbornness that can afflict the Christian and non-Christian alike), simply trace the lonely fruits of an unwillingness to enter into real worship.
The remarkable idea that good gifts that actually obligate and rehumanize us at the same time is often foreign to Western culture and thought, because (following Kant's half-baked way of thinking about gifts), we've supposed that the only gifts that are genuine are those that are given disinterestedly.
It's not a coincidence that atheism is frequently eager to deny that we can know who in the world the creator is and impugn God's integrity at the same time. If either project is successfully sustained, then the atheist can "conveniently" and effectively minimize, shirk, or belittle the goodness of God's gifts, or the astonishingly arrogant treachery that's bound up in a refusal to worship God as he actually is.
Remarkably, God still delights in giving atheists good gifts of his grace (Matt. 5:44-45). He also delights in drawing them into the remarkable journey of a life that begins to sense the rehumanizing joy of worship.
See John Barclay's books, Paul and the Power of Grace or (for a more academic discussion of gifts), see Barclay's Paul and the Gift. Both are worth their weight in gold.