Quite frankly, this ignores many, many other factors. Chief among the reasons this is not true is the simple post hoc ergo propter hoc fallacy. Just because one thing happens after another, doesn't mean the second event was caused by the first event.

There have been many countries whose Jews left who did not lose their powerful status. Turkey was not a superpower when it was oppressing Jews, and it was actually fairly good to Jews by the time it was already firmly in decline by most accounts, and Jewish immigration did occur to Turkey prior to WWI. Turkey being, of course, the Ottoman Empire at the time. Jews were oppressed by the Romans for quite some time, but the Romans persisted very strongly for quite some time after. And that's the tip of the iceberg.

There is something to be said that perhaps expelling Jews is indicative of a regime that is brutal and thus destined for failure due to lacking popular support, but even that is a tenuous assumption. History doesn't really agree with that poster. There's far more at play in each case than whether or not Jews were oppressed or left a country.

There are a number of problems with that idea. For one, the defeat of the Spanish armada was quite definitely not tied to a lack of Jews. I'm not entirely sure how to support a statement that simple with sources, but it should be self-evident.

For another, the time between 1492 and 1588 is a huge era when we're discussing the Spanish Empire of the period. In that timeframe, they managed to conquer the Inca, the Aztecs and even most of the remaining Mayan states. Their empire expanded to encompass the lands from Peru to modern Texas and from the Philippines to Florida. By their defeat in 1588, the Spanish were a preeminent world power and continued to be so into the late 16th century. By the beginning of the early 17th century, Spain was wracked by plagues. By the mid 17th century, profits from the American colonies were swiftly falling and unrest was growing in Europe. Inflation due to economic policies and a massive plague led to the Catalan revolt in 1640, which is a good place to mark the beginning of Spanish decline. I go into more detail about the progression of this decline in a previous comment.

The timeline for "the Jews leaving" simply doesn't fit with an actual timeline for the decline of Spanish power. The correlation is at best mildly related and more probably, just idle speculation. I would similarly hesitate to draw further conclusions as to the effects of Jewish diaspora. The results are going to depend on so many factors as to be nigh unpredictable.

Aside from what /u/tayaravaknin has pointed out, the idea that the expulsion of Jews from Spain in 1492 is in any way related to the decline of Spain as a superpower is comically inaccurate, because 1492 is usually as the symbolic starting date of Spain as a superpower in the first place. Following the establishment of an overseas empire after the voyages of Columbus and the unification of most of the Iberian peninsula, the Spanish (under the Hapsburg family) emerged into continental Europe as a major military power and fought with France for decades. Dating the "decline" of the Spanish Empire is problematic anyways, but the traditional starting point for the beginning of the end for Spain as a dominant force on the European continent is the Battle of Rocroi in 1643, a full 65 years past the OP's suggestion of the 1588 defeat of the Armada. The loss of most of Spain's overseas colonies would only come in the 19th century, over three hundred years past the expulsion of the Jews at the end of the 15th century. The attempt to connect Jews with the rise and fall of Spain as a major international power is nonsensical.