In Orthodox Judaism, based on Biblical passages, the Sabbath was given to Israel. As you mention non-Jew’s are neither expected nor encouraged to keep the Sabbath.
That being said, despite the popular notion of a “Shabbos Goy” it is generally forbidden in Orthodox Judaism to benefit from a gentile’s violation of the Sabbath. One is certainly forbidden to tell a non-Jew to break the Sabbath.You are not allowed to have a non-Jew turn on the light for you and he did it without being asked you may not utilize the light. While there are some exception most of them have weak support. A notable exception is a great deal of leniency was practiced with regards to non-Jew’s starting fires on the Sabbath to heat homes, since this could be a health issue.
It’s not just against the “spirit of the law”, it is against the letter of the law in Orthodox Judaism.