The trailer, at least, was apparently made with Sucker Punch’s engine.
One of the biggest time and money sinks for Metal Gear Solid 5 over the course of that game’s development was the engine- Kojima poured in a lot of time and money into the FOX engine, making it modular, flexible, and scaleable, with the intent of using it for all future Metal Gear games, and shortening development time on future games considerably.
Of course, he never got to do that- and it is unlikely that he will use FOX Engine for his upcoming game, Death Stranding. Which means that Kojima either has to make a brand new engine from scratch, again, or use one that already exists.
A lot of Japanese developers these days have begun to use Unreal engine- which makes sense. It is a well documented, easy, powerful and flexible engine, after all. So you might have expected Kojima to go with Unreal as well. However, according to a report by popular YouTuber YongYea, attributed to unnamed sources, Kojima may instead be eyeing the engine that Sucker Punch used with their 2014 game inFamous: Second Son. At the very least, it seems apparent that the trailer for the game was made in that engine.
The engine used in Second Son, which was a technical marvel, would certainly lend itself to Kojima’s uses- it can evidently render a vibrant and dense open world for an action game, all the while looking good, too. That is, apparently, the kind of game that Kojima wants to make, so this report does make some sense. That said, take it with a pinch of salt and all that for now- there’s nothing official on it either way.