First of all, this code is fishy: @Autowired on fields, reassigned method argument.

And if you ask my opinion, this code doesn't need neither Streams, no Optional (since there's no method involved which return one). It seems like you were asked to rewrite the code in an obscuring way so that it would abuse either an Optional or Stream.

Number of lines is not a metric for code quality.

Here's an example of a Stream-abuse:

Copy@Override
public ResponseDto addGameToSession(GameDto gameDto) {
    
    Stream.of(gameDto)
        .map(gameplay::playRandomGame)
        .forEach(gDto -> repo.updateTotals(gDto.getResult()));
    
    return sessionRegistry.addGameSession(gameDto.getSessionId(), gameDto.getPlayer1Choice(), gameDto.getPlayer2Choice(), gameDto.getResult());
}

The code above unnecessarily operates via side-effects, which is disparaged be the Stream API documentation.

And here's an example of an Optional-abuse (it can be more frequently observed with Optional.ofNullable()):

Copy@Override
public ResponseDto addGameToSession(GameDto gameDto) {
    
    Optional.of(gameDto)
        .map(gameplay::playRandomGame)
        .ifPresent(gDto -> repo.updateTotals(gDto.getResult()));
    
    return sessionRegistry.addGameSession(gameDto.getSessionId(), gameDto.getPlayer1Choice(), gameDto.getPlayer2Choice(), gameDto.getResult());
}

In a nut-shell, Optional is a container of data, which is intended to represent a return type. You can wrap it around something nullable and that would allow to interact safely with a result of a method call regardless whether it contains the actual value or not.

Creation an Optional only in order chain methods on it, goes against its design goal. It's a smell and should be avoided.

Regarding the usage of Optional, see this and this answers by @Stuart Marks, Java and OpenJDK developer.