I think this statement mixes up "productive" and "useful". In this sense Antidote47k is right that gold has some very similar properties that make it useful, first and foremost that it is independent from any specific entity to continue to exist and "provide services" as it does now.
The essence of "productive" for me is the effect on the rest of the economy. "Usefulness" as a store of value is another story.
First let's look at "productivity". What would happen if Central Banks and private treasuries sell all their gold and it crashes 90% or more? You already said it: the mining sector could change. But gold's importance as a "store of value" is much higher than the share of the economy that is directly affected by gold, and I've already mentioned that a lower gold price would also lower the cost of the industries that need gold as an input. So the only direct negative impact of a very low gold price on the economy may be on mining and financial sectors (in the financial sectors, only those entities significantly involved with gold storage which could not replace gold activities with Bitcoin activities), and thus be very low overall. This means that gold directly doesn't contribute much to the economy.
Regarding the "usefulness", the problem is that it depends all on its valuation. If Gold was worth less it would be also less useful. I see the gold industry very much as a circular process, a virtuous cycle based on tradition. If this cycle is broken, then it could collapse entirely. If gold crashes 95%, would your grandma still consider it a good investment? (Maybe if she's a contrarian ...

). This problem is shared a bit with Bitcoin.
If the gold price were to go down, not only mining would go down, but recycling would go down. Now what happens to artisanal gold mining when the margins drop? I don't know, but the more I think about it, it may harm the people and artisanal mining would go up as they use basic tools, low fixed costs and often dramatically low labour cost. While some parts of nature may be better off because heavy machinery gets shut down, the poorest of the poor may get even more exploited.
I personally think if gold crashes 90-99% "back to its industrial usage price" then artisanal mining would also go down a lot. Artisanal mining only makes sense if gold is an essentially higher valued good than other materials. There are also studies that show that when the gold price increases, artisanal mining also increases, see
this article (artisanal gold production doubled in the gold bull market of 2002-2010). It's imo more likely that a lot of industrial gold mines would shut down, with about 10% remaining - but these 10% would be the most efficient of the market.
Regarding recycling, according to my Google search it seems to be significantly cheaper than mining (about factor 5). I think thus this sector would be less affected than mining in this case.
For example. Gold is a raw material, for example, for the jewelry industry. Consequently, gold creates highly skilled jobs (jewelers).
I would argue that jewelry could be less affected by a "replacement of gold by Bitcoin" with subsequent gold crash. While gold jewelry is also a store of value, it has also "physical" qualities which will generate a lot of demand even in the case of a 90%+ gold price crash. The only problem I can imagine is that it could be temporary hit by panic sales of people who use jewelry as a store of value, but then it could stabilize. Perhaps on a slightly lower level than before, but I think the major impact of a "gold price collapse" would be on financial services like gold bar storage.
But, for example, buying or selling stocks does not create any added value in the economy, it merely redistributes it speculatively.
Stocks are one of the main ways for companies to grow. That's what I meant with "productive". "Selling" stocks of course is not productive, but the amount of capital in the stock market, in our current economic system, is a good indicator for the capital cost. If people invested less in stocks, it would be more costly for companies to grow, and we would have less innovation.
Regarding mining industry (which would be affected) and electronics (which would not be affected at all by a gold market collapse), see my answer to @tiCer.
Where does Bitcoin create jobs? Exclusively in the financial sector, that is, where surplus value is not created. So, roughly speaking, Bitcoin cannot contribute to the growth of real GDP, while gold can.
The surplus value from Bitcoin comes from the efficiency as a tool to transfer value. And this affects all companies which transfer value.
Take international trade: if using Bitcoin for transfers costs less than SWIFT, then all companies active in international trade would be benefitted by using Bitcoin. Or another example: online payments. Merchants have to pay a significant amount of fees to credit card companies. If instead Bitcoin (e.g. via Lightning or Ark) would be massively used, this would reduce the fees. (Regarding the relevancy of intermediaries, see below).
There's a catch: all these use cases depend on a lower BTC volatility, but in the scenario I describe this would be the case.
What matters is that gold is a "physical commodity", and therefore it can participate (as raw material) in the creation of other goods, which means it can create surplus value and thereby contribute to economic growth.
Again, if the price of gold collapses because it is not longer used as store of value, its industrial uses would remain, so no jobs/industries would be lost there (only in mining and financial services).
These intermediaries contribute to the economy by paying taxes and employing citizens. If Bitcoin displaces these financial middlemen, government revenue through licensing and tax, it will reduce and it might cause unemployment.
Here what we have to look at is: we have to compare potential efficiency gains by cutting out the intermediaries, which has an effect on the whole economy (i.e. costs for financial transactions decrease, and inflation goes down) and the impact of the loss of these industries.
I've not analyzed it in detail (if you want you can), but if all major credit card businesses employ less than 200,000 people (Visa and Mastercard have about 30,000 each), but at least a billion people are affected by the cost of the credit card fees, then I think this is a strong hint that the efficiency surplus is higher than the impact the loss of these companies would have on the economy.