Yes they did. You could vote in the referendum from abroad (I did). There's no such thing as EU citizenship anyway, so nobodies citizenship changed as a result.
Well just go ahead and apply to Brussels to get your EU passport back then?
Obviously you can't, because there's no such thing as EU citizenship. It doesn't grant citizenship, and cannot because that would require it to be an independent nation recognized by other nations as such. There is only citizenship of member states. Playing with words doesn't make something real, it only confuses people.
You’re right indeed that there is a real legal concept in EU law called EU citizenship, which everyone with the nationality of an EU member state holds. The other commenter is wrong on that point.
But the other commenter is also right that there is not the kind of independently existent EU citizenship that would persist when one ceases to be a national of an EU member state - it gets lost in that case even if the reason for this change is not an individual loss of the member state’s nationality but because the member state withdrew from the EU. The ECJ definitively settled this last year. Nor are EU passports issued on the basis of EU citizenship, nor would EU citizens typically include “EU” as one of the answers if they are asked by a government to list all their citizenships or view themselves as dual citizens if their only national-level citizenship is from a single EU member state.
For several reasons like this, it’s not at all unreasonable for the other commenter not to view EU citizenship as a real citizenship of its own, despite the use of the term under EU law.
Personally, I view the term EU citizenship in part as a briefer shorthand for “national of an EU member state” - including in the definition whatever edge-case handling is appropriate for each country’s special-case territories, and therefore more precise in a predictable way. Beyond that, it’s just a symbolic reflection of the EU’s official aspirational policy goal of ever closer union.