Finding non-linear editors on a computer can be really hard. The linear approach in the old days was actually a forced limitation due to the restrictions you had with tapes. You needed to add clips successively. Sure, you could make an insert but at the risk of messing up the time-base and other things.
That being said - the non-linear/linear is not the reason why editing struggle on a less capable CPU. To the computer it doesn't matter at all in what succession clips comes in so implementing a restriction such as linear approach has no point.
The main reason for what you experience comes from the the resolution of the video, its compression codec, the disk capabilities and memory available for caching the video/sound. If you work in HD the amount of raw data is many times that of f.ex. NTSC/PAL and naturally gets harder to process for a computer.
You will see these problems in any editor as the common factor is the computer itself. The Adobe suite and other professional suites can do a lot of things with a video, but as long as you don't utilize effects and so forth there is really not much load on the computer besides from processing the video itself.
The professional software has also addresses performance issues to get the most out of what is available. The risk is actually to loose performance with very basic software that do no pre-processing of the video and sound to enable it run smoother, implementing smart optimized caching, not to mention utilizing a GPU and so forth, and only relies on loading from disk as-is.
The (permanent) solution is to upgrade the hardware or run the software on capable hardware.
Tip to get around with a less capable computer:
Before starting to edit you can reduce the resolution of the original clips to a low-res version. Then edit with these in that resolution. When finished create a new project set to the resolution of the final product and import the original full resolution clips and an edit list. This way you can work with low-resolution on a less capable CPU.
See EDL files or OMF interchange files or AAF files (what suits best), and refer to the software's manual on how to export and import edit files. You might need to rename the clip names in the file to point to the full resolution of the clips so have a naming convention ready from the beginning when importing clips from the camera to make life easier.