Lagging clips when inserted in premiere pro

 Please use the free MediaInfo and post a screenshot the properties of your media in tree view:

MediaInfo 

Screen capture software often records in VBR which is not great for editing, regardless of your PC specs. Can you check your recording settings and make sure you are recording in CBR?

The key to a good video editing workflow is finding a good balance between edited master settings, edit settings and source footage settings.

What software or hardware are you using to make the screen recordings of your game play?  What file format is being created?

A challenge with some screen recording options (both hardware and software) is the resulting file is what you would call an end-user file.  That is, it's just meant for playback and not meant to be used as source.  The muxed MPEG2 video stream from DVD-Video is a good example of this and so are low-bandwidth MP4 files.

If I plan to edit my screen recordings, I usually go with ProRes422 LT or ProRes422 HQ (it depends on the intended use) for the video exported format from the screen recording software or recorded by the screen recording hardware.  As ProRes is a mezzanine CODEC for editing, this works really well in Premiere Pro in a Sequence set to ProRes which exports extremely well to ProRes, but also well to H264 and HEVC.

As a test, you could try transcoding a few of your clips to ProRes using Adobe Media Encoder (it's under the QuickTime presets), import those into Premiere Pro and create a Sequence from those clips.  One thing to note is that ProRes at 1920x1080 is about 1GB per minute.  Also, your current clips may or may not hold up well to being transcoded.  If not, you'll notice it right away with diminished picture quality and maybe diminished audio quality.