Why use a single engine plane instead of a multi engine one for a long range flight record?
As said in the comments, in a distance record aircraft you want to keep the drag and mass of your aircraft as low as possible. The previous and next record were flown in single engines too and risk assessment was a bit different back then.

Using a single engine for such long distances wasn't the only ANT-25 characteristic you wouldn't see in a normal airplane: the engine was underpowered (only Russian production engine available?) and for record flights the whole aircraft was even lack-stripped in order to weight less.

For emergency landings in the arctic they had skis, tents and other gear stored in the wings.

In the case of having to land on water they would jettison part of the fuel and inflate some kind of balloons which were inside the wings. That way the wings could be used as floating bodies and prevent water from entering. After water-ditching with retracted landing gear the aircraft could apparently stay afloat for a long time.

If you're interested in further details this biography of Pavel Sukhoi describes the project thoroughly in one of the chapters.