Yup. Actually, Iran was the 13th largest economy by nominal GDP in 1980.
Most of the growth happened in the last 10 years of the Shah after the establishment of the OPEC, which increased oil prices from $5 per barrel to about $20 per barrel.
However, the video is not a correct representation of all of Iran prior to the revolution. While Iran was doing very well in large cities, the situation in small cities was not good. If you want to compare today's Iran to Iran before the 1979 revolution, these are the main points:
Iran in 1970s:
1. Literacy rate was 35% with a huge gender gap. Only 24% of Iranian women were literate, while 48% of Iranian men were literate.
2. Urbanization rate was also low. It was about 34%.
3. Fertility rate stood above 7.
4. Tourism was flourishing with most travel agencies in the West offering Iran as the first choice of travel. You could find Europeans and Americans all over Iran all the time. Some of them even immigrated to Iran and stayed here.
5. Iran had some huge industries, but we relied on the US for nearly all of those industries. We mostly assembled stuff. But our productions were of high quality, because the designs and raw materials came from the US and Europe.
6. The Iranian culture was quite influential. Our singers were well-known throughout the region. Our cinema and TV shows were quite well-known and popular too. The extent of our music industry was so much that even decades after the revolution, people in the region continue to listen to our old singers like Googoosh, Hayedeh, etc.
7. Iran was good at sports, but we weren't really a powerful country in sports.
8. The quality of education was good, but only few people were really interested in math-intensive sciences. Most people preferred easier educational paths.
Iran in 2020:
1. Literacy rate for all of the population is now 86% with no gender gap. For people under the age of 60, the literacy rate stands at 97%. Gender gap is nearly zero, even in rural areas.
2. Urbanization rate has increased to 76%.
3. Fertility rate is fluctuating between 1.8 and 2.1 in recent years.
4. Iran is no longer seen as a tourist spot. Most travelers to Iran are from neighboring countries. Usually, they are Iraqis or Shiite pilgrims, or people who are really interested in history and politics.
5. We have developed indigenous industries that work without reliance to foreign countries. Our industrial base has grown and it is much more domestic than prior to the revolution.
6. The Iranian culture has lost its influence in the region. The regime has changed Iran's picture from an Iranian country to an Islamic one that promotes Islam and defends Palestine against Zionists. Our cinema continues to remain one of the best in the world. In fact, the quality of our movies has improved greatly after the revolution, but our music industry is dead.
7. Iran is good at most sports today. Our football team is 22nd in the world. Our volleyball team has been in top 10 many times. Our basketball team has been in top 20 for a long period. Our wrestling, weightlifting and Taekwondo have become World champions several times. Our best result in the Olympics was 12th in the 2012 Summer Olympics. Overall, we are doing better in sports.
8. Iran is excelling at education and science. We have one of the world's largest number of engineers and graduates in STEM fields. Our teams in science Olympiads have done extremely well. For example, Iran was ranked 1st in International Math Olympiad in 1998 and 3rd in 1997. We have won the Fields medal (the highest award in mathematics) two times in a row in 2014 and 2018.
9. GDP per capita has increased since 1979. But considering the international trend, that's not impressive at all. One may argue that Iran's economy has stagnated after the 1979 revolution, but one should also take 8 years of a bloody war with Iraq into account as well.
I think the major difference between today's Iran under the current regime or the previous regime is that today's Iran would've been more liberal and we would've had a huge income from tourism. We also would've sold 5 to 6 times more oil than now. Iran could've easily entered top 10 economies of the world under the reign of the Shah. So, your comparison with Japan is accurate.