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That article talks a lot about gamma and options, but doesn't mention volatility once.
The primary pricing factor for options is volatility - And as more people buy volatility / gamma / options (you could use any term in that context), the volatility should rise, making options more expensive.
Sure - as more call options are sold, the more underlying will need to be bought to hedge (by the seller - the buyers are still unhedged.) - not quite in the way you suggest though - the hedge will cover both losses and exercise.
Also not mentioned in the article, it's a moving target - as your stock price rises, your option pricing will change - this time because of the increase in actual volatility driven by the changing underlying price (the corollary of vanna & volga in old school options pricing) - again, upwards.
With a rising price, you might expect demand to fall
I get a sneaking suspicion that the underlying model assumptions aren't holding true any more, or that something else is happening.
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NotThamesWater
@Arducius
Call options and people covering their positions using the same stock the option is for.
Basically buying two shares for every option you sell, one to sell at the agreed price and one to cover your losses (as that asset is appreciating in value at the time). I only have s rudimentary understanding of this tbh but saw this article on it the other day:
https://www.forbes.com/sites/georgecalhoun/2021/03/10/gamestop-the-second-surgeanatomy-of-a-gamma-swarm/amp/