The two trillion they refer to is Market CAP of public traded companies, thus they literally say it devalued the stock market for two trillion.
Anyways, there was a lot of leveraged speculation involved and / or institutional investors, i strongly doubt the average joe sat awake at night (in Europe) and just waited to press sell (and everybody in the same 5 minutes).
Joking by side - my indicators drew the picture that in majority only stocks included in indices where sold off.
In the end it appears that leveraged speculation wiped of a large part of that stack (to speak in that language), even "solid" names dropped on EU open up to minus 20% (villeroy & boch ag for example, just to climb back to minus 2% (FLASH CRASH INDEED) ) -- it also appeared that leveraged speculators sold pound vs gold once it was clear that leave wins the vote..
Of course while the initial reaction appears to be facilitated by leveraged HFT, the brexit is expected to have negative consequences for trade in the UK and for EU countries. There is no fixed plan how the brexit would happen and if tariffs and trade deals change in a negative way for the economy. For the long run there are also talks about loss of GDP between ~ 6-9% (All speculation, the guy with the crystal ball please raise your hand).
Bottom line, lowered economic outlook, uncertainty and speculation very likely worked in a combined manner to "Wipe OFF" .