Shaitan is not the enemy of just Muslims. It is the enemy of the whole mankind.
O mankind, eat from whatever is on earth [that is] lawful and good and do not follow the footsteps of Satan. Indeed, he is to you a clear enemy.
....Indeed Satan, to man, is a manifest enemy.
Shaitan misguides the whole mankind in the ways very similar to how it misguides the Muslims: by dragging them both away from the truth (Islam)...
[Satan] said, "Because You have put me in error, I will surely sit in wait for them on Your straight path.
...and by making the wrong things attractive to them.
Satan promises them and arouses desire in them. But Satan does not promise them except delusion.
But it is of course more easy for Shaitan to misguide Non-muslims and the weaker Muslims.
His power is only over those who obey and follow him (Satan), and those who join partners with Him (Allah) [i.e. those who are Mushrikun - polytheists.
ۚ وَاللَّهُ عَلِيمٌ حَكِيمٌ (And Allah is the All-Knower, the Wise)
اللَّهُمَّ انْفَعْنِي بِمَا عَلَّمْـتَنِي وَ عَلِّمْنِي مَا يَنْفَعُنِي