Although AB contains many links to news stories, it's not a 'news aggregation' service, per se. So it's unlikely that the proposed legislation could affect AB. Also the proposed new rules also have to be inserted into national legislation by EU member states which, assuming that Brexit actually happens, won't include the UK anyway.
However any UK legislation that might come into place (or, indeed, any that is already in place) will (or does) cover UK-based websites, irrespective of where the content on those sites is hosted. For example, the editor of AB (which is based in Kettering) has to ensure that posts on this site don't contravene British sub judice rules, even though those posts are actually hosted on US servers.