Program to save videos??

OBS Studio works for my needs. May need some tweaking video/audio sync depending on the game. Duration of video is not very relevant when looking for such a program..

"It's simple. In the Play Games app, select any game you want to play, then tap the record button. You can capture your gameplay in 720p or 480p, and choose to add video of yourself and commentary via your device's front facing camera and microphone.

If you are using an emulator to play it on PC just google screen capture software.
If you want to capture off of your phone, not sure the best way to do it.

On Android I used "DU Recorder". (https://du-recorder.en.uptodown.com/android)
You can use also video grabber like Elgato (via HDMI with special connector).

On PC I suggest you to buy any of the program to edit the video (similar to Vegas).
You can also use free software like Blender, Hitfilm etc. (https://www.oberlo.com/blog/best-free-video-editing-software)

a simple way is BlueStacks (emulate then record)
if you have a rooted phone there are some capture apps

These 2 can both backrecord up to a few minutes should've you had manual recording off.
If using NVIDIA GPU, Nvidia Shadowplay

If using AMD Radeon ReLive

If you just want to capture as you go
Streamlabs OBS

BTW for anyone reading this and interested in video montage, including OP, I'd like to recommend free and open source program called Avedemux. It's very primitive, but the main feature of it is that it's able to cut videos without reencoding them. So if you just need to take a long video and cut out some part of it, it's perfect for this task as it will be much faster than in any other software.