Undoubtedly, Xbox One and Playstation 4 have several processor cores that make them so powerful for hardcore console gaming but there are already official workarounds in making console streaming smooth ever since the Playstation 3 era where you can use Playstation Portable or Vita to remotely stream Playstation 3 console through Remote Play and it's the same for streaming Playstation 4 on the Playstation Vita as well using the same method. There was also Remote Play feature for PC that allowed you to stream Playstation 3 games but that was for some Sony-branded computers. Unofficially, there was a similar program for non-Sony-branded computers that allowed you to do the same thing but it may probably defeat the purpose of competition as it may look like an unofficial third-party solution. Those I mentioned above were official methods and it's the same for Xbox App for Windows 10 which is the official streaming method by Microsoft where you can stream Xbox One system on a computer running Windows 10. I guess that your computer must be seriously powerful enough to stream Xbox One system as a Remote Play feature.
Then, there is an unofficial Remote Play feature for PC that allows you to stream Playstation 4 games. However, there are already doubts that Sony will sue the person who's making this feature and besides, it's looking third-party-ish if you ask. There was an Android version which is free but the PC version will be paid which is kind of bullshit. Xperia devices have the official Remote Play feature but mixing console technology with smartphone and tablet technology isn't going to help and Playstation for Android was already a flop that Sony went back to focus on console part which is already a big hit again thanks to Playstation 4 being done right although the Playstation Vita is made a legacy in the West but popular in the East and it is kind of like Sony's version of Saturn or PC-Engine.
Funny thing is, my first discovery about this feature came from Lazy Game Reviews' tweet about it. Perhaps, DOS gaming and classic computers were the reasons I discovered and subscribed to Lazy Game Reviews' YouTube channel but I don't know if I may get interested in playing DOS games one day in the future. There might be some DOS games I played before in my childhood but now, things have changed and somehow, some of the DOS games couldn't even work correctly back then.