This is a fascinating question, and one that I think modern economists don’t think about enough. To start with, we must face the most salient confusion of most popular economic debates: definitions. People often use the term “command economy” and “planned economy” interchangeably because they both convey a sense of “the government tells the economy what to do”. But, as it turns out, there are many different ways in which a government can influence and direct an economy.

Let’s compare two different frameworks. During the Second World War the US solicited most of its needs through contracts often with open bidding by firms. But those firms were subject to resource priority constraints imposed on the War Production Board on access to vital war materiel (e.g., you can’t get, say, aluminum or tungsten or tantalum unless your project has an adequately high “priority” letter grade). Your workers would be hired in the open market and paid competitive wages they could spend in the economy however they pleased. However, consumer purchases were subject to rationing under the Office of Price Administration (later the Office of Economic Stabilization). So purchases of food, tires, gasoline, clothing, were made with money but had to be accompanied by a “stamp” for that good from a monthly ration book. In addition to stamp-based rationing, the OPA / OES also had power of price setting, which they sometimes used.

(There are a few exceptions to this hybrid market / command framework in the US. In critical industries with simple supply chains and deep labor problems, the industries were “temporarily” nationalized to become government run entities. The best example of this is probably the decision by the US, and UK, to nationalize the coal mining industry. This was mostly a union-busting measure, though very much not dressed as one at the time. Just understand that this was a very rare practice for these countries during the war.)

For comparison, in the USSR the the state had total authority over economic activity. The state could assign individuals occupations, set prices, allocate resources, et cetera all by fiat if they chose to. (The Soviets had theoretical rationing, but the consumer good economy ceased to exist during the war. Most workers were effectively paid in food and shelter.) The problem with absolute power in an economic setting, though, is that gaining it seems to be easier than using it. A modern economy is a titanic organizational puzzle, especially in an era of postal correspondence, typewriters, and yellow note pads. Therefore, the Soviet economic managers delegated as much of the organizing as they could to “market-like” institutions. During peacetime Soviet design firms / bureaus would “bid” on contracts at a certain price in a pseudo-market framing. However, in the crisis of 1941, many firms found themselves simply told what to produce, where to produce it, and the state provided the (often inexperienced) workers and their rations.

In some ways, using the USSR is a bad example because even now it’s not all that clear what was going on in 1941-1942. But the USSR is usually held up as the “purest” example of a planned economy in WW2. And whatever the ambiguity about policies and implementation, it gives a clear sense of the gradient of “degrees” of command economics. By modern standard, the US during WW2 was much more of a command economy than China is today. The US controlled consumer goods access, regulated prices, centrally planned certain aspects of industrial production, and in a few cases took direct control over labor. It was probably more of a command economy in 1942 than Nazi Germany was at the same time (one of the weird puzzles of the war is that the Germans waited until quit late to halt consumer goods production and adopt a total war economic plan). It was very similar to U.K. industrial management. And it also had a great deal in common with that of Japan, though losing nations always reached a degree of desperate direct control the victors didn’t seem to match.

As for the rest of your question, the argument you are quoting from YouTube is not a good one. Probably the most interesting unanswered question from the US economy in WW2 is: does command economics make sense in an economy with slack capacity? (“Slack capacity” in this case referring to vast unemployment the US still had from the 1937-38 Recession.) We don’t have a good answer to that, I don’t think. It’s actually something I’ve always wanted to write a paper about. What we do know in the economic profession is that command economics seems to be a spectacular failure in fully mobilized economies. To understand the difference, consider other nations that adopted similar policies during the war. The U.K. continued its command economics policies several years longer than the US and still did not enjoy great prosperity, to put it lightly. The Soviet Union, the greatest command-economic experiment of all time, had an interval of postwar growth, but by the 1960’s was falling far behind. In both cases, the reason why command economics did not save them from economic stagnation is easy to see: command economics gives you the power to order people to do anything, but it doesn’t (i) guarantee your orders will be carried out and (ii) tell you what you should be trying to do. But these are deep abstract questions that stray too far from this subreddit. Suffice to say, don’t get your economics from YouTube.

In addition to u/Prosodism's excellent comment, I'd like to add that the way we measure the contribution of manufacturing to GDP differs depending on whether a particular manufacturing activity is producing output intended to be sold on the market, or not (non-market).

To take, say, a car manufacturer, the normal way of valuing their contribution to GDP is to measure the sales of cars minus the operating expenses to create those cars (intermediate consumption in GDP speak). So, if a car manufacturer sells $100m of cars and spends $20m in buying steel and electricity and the like to make it, then the contribution to GDP is $80m (which is then divided between compensation paid to employees, mainly wages and salaries, and the return to capital, known as operating surplus). 

If the car manufacturer hired Homer Simpson to design the car, it cost $20m in intermediate consumption, and it's a dud, and they only sell $1m of cars, then the contribution to GDP is -$19m ($1m - $20m). 

This is well enough for things intended to be sold in the market. However, for things like military production in WWII, obviously the Germans and the Italians and the Japanese were not going to be paying for bombs and artillery shells and the like to be delivered to them at high speed. And, more peacefully, how do you value say publicly-funded education? So for non-market production, the contribution to GDP is valued at the sum of the compensation paid to employees + an estimate of the consumption of fixed capital. 

This has the unfortunate consequence that no matter how badly nor how well the government produces something, it still has the same contribution to GDP. 

Consequently manufacturing production levels during WWII could easily look very high, because the government was paying for most of it regardless of whether it was a good deal or not.  

The proper treatment of military spending, and government spending, was quite a controversy when the concepts of GDP and GNP were being developed in the 1930s and during WWII. Simon Kuznets, the American economist who won a Nobel Prize in 1971, in part for his contributions to the development of national accounting, changed his view on this over time, in 1941 arguing that military expenditure should be included, just as private spending by corporations on security was included, and therefore that of local police. However, in 1945, Kuzents argued that military spending should be counted in national product during a time of total war but should be excluded in peacetime and instead considered as part of intermediate consumption. 

On the other hand, if we regard GDP as a measure of the productive capacity of the economy, which is often important for government budgeting, then the ability to produce artillery shells is as valid as that to produce cars. 

For some reason this history has gotten simplified as Kuznets arguing for leaving military spending out of GDP. (I actually didn't realise the complexity of Kuznet's position myself until I checked my sources for this).  

This may be what the YouTuber was referring to in talking about a "fake manufactured boom". 

Sources

United Nations., European Commission., International Monetary Fund., Organisation for Economic Co-operation and Development., & World Bank. (2009). System of national accounts 2008. New York: United Nations. https://unstats.un.org/unsd/nationalaccount/sna2008.asp

see Chapter 6.4 Market output, output for own final use and non-market output, particularly paras 6.128 - 6.132. 

Rockoff, Hugh. 2019. “On the Controversies Behind the Origins of the Federal Economic Statistics.” The Journal of Economic Perspectives 33 (1): 147–64., pdf link - https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.33.1.147