Is it correct to say that wealth is "destroyed" when an asset bubble bursts?
We need to distinguish two things here: the intrinsic value of the assets, and their fair value, or market value.

No matter how much the price of an asset changes on financial markets (say, stock exchanges), its intrincic value stays the same, all other things equals. Typically, you could use the cost of the asset to assess its intrinsic value: for a house, the price of its construction. For a share, the book value per share of the underlying firm. For bonds, the nominal (or face value) amount.

But assessing cost is sometimes tricky. The book value might incorporate things that are valued at fair value. For real estate, the price of the land is a large part of the total cost, and it changes all the time. For bonds, you could incorporate interests and discount them, but you need to choose a discount rate.

Thus we typically assess wealth using fair value. It's a concept precisely defined by IFRS (IFRS 13 - Fair value measurement). Basically, the fair value of an asset is the price at which you could sell it under normal market conditions ('at arm's length'). It is true 'value', as you could trade the asset against that amount of cash.

To come back to your question: wealth is measured at fair value, or market value. Therefore, the $34.4bn were indeed destroyed, or disappeared, even though the intrinsic value may have been constant. Your second suggestion is correct.