Well, aside from being a counter-factual, this kind of claim is very similar to what on /r/badhistory is simply referred to as "The Chart" and is regarded as being an especially ludicrous sort of nonsense.

It's a fundamental misunderstanding of how science works and proceeds.

In the specific case of Spain, what was it about being in Spain that or being removed from Spain that supposedly prevented this advancement from occurring? Was some set of knowledge lost? Were critical scientists killed in some sort of devastating way? The reconquista wasn't exactly pleasant, but the basic answer is, no, the reconquest of Muslim Spain did not involve some sort of loss of knowledge that would have made up for 200 years of advances in physics, chemistry, engineering, rocketry and the related fields that would have gotten us to the moon in 1769. Such a claim is prima facie absurd.

Moreover, when we look at the relative decline in Islamic science with what's going on in Europe it's clear to me at least that there are more important developments that were happening elsewhere that slowed scientific development. Resistance to the printing press in the 15th century certainly did not help things. Nor did the rejection of the neo-platonist falsafa tradition as espoused by al-Ghazali (who is oddly name-checked in the video), such that specifically in Spain philosopher scientists like Averroes (Ibn Rushd) found themselves banished by their own Muslim rulers.

I personally think one important distinction between the origins of the scientific revolution that would take place in Europe and what ended up happening in Islamdom is that while both Christendom and Islamdom saw the massive spread of institutions of higher education in the Middle Ages in the form of universities and madrassas respectively, it's only in the universities that a specifically secular and scientific field of inquiry is developed. So madrassas and universities produce brilliant minds, but the madrassas are not producing natural philosophers and scientists.

I think the message of the video is a lovely sentiment but it ignores the extent to which Islam had in many ways already begun to look in on itself prior to the reconquista in ways that crippled its ability to partake in the kind of scientific revolution that happened in Europe.

Edit: also, in terms of destruction, it's the Mongols, not the Spanish, who really mess things up in Islamdom, but I think it would be easy to overstate the extent to which the Mongol conquests "ended" the "Islamic Golden Age". The scale of destruction involved in the Mongol conquests may have been in part necessary for the inward turn of Islam after the 13th century but it was by no means sufficient.