The main take-away that I had is that the courts generally uphold "the people" to mean "citizens", but there are some strong divisions on that and the case is far from settled. At the very least I agree with Harvard's opinion that this judgement cannot hold true to all instances of the the phrase "the people" without massively undoing hundreds of years of case law.
Based on that I will change my statement here to say "the Constitution restricts the government, but it's unclear in the courts whether it restricts the government's actions against non-citizens, although it probably should according to constitutional law scholars". So if you're a tourist in the US, watch what you say and do, because you may not have any right to freedom of speech or protection from unreasonable search and seizure.