There's no such thing as 'no ESR' electrolytics - the one you have in the picture is seriously faulty, and reads so low for capacitance that ESR would be pointless, hence it doesn't offer a reading.
Sounds like they are speaker coupling capacitors, used back when single supply rails were the norm - and really makes little difference. A single supply amp uses two capacitors, one for the PSU, one for the speaker. A dual supply amp uses two capacitors for the supply. In either case the audio travels through all the capacitors.