I have heard you can strip the top-coat down and just restain. The cabinets are so old, it doesn’t look like there is a top coat.
You can strip off the remaining top coat and restain. This will work and will produce good results. The most difficult part is removing all of the top coat. If any remains when staining then some blotchy areas will develop.
Another option is to clean (very good cleaning), sand with 180 grit sand paper or fine sanding sponge then restain with a gel stain or a heavy bodied penetrating stain. The gel stain will produce the most consistent results.
Take a look at this question I answered for more info in this technique, <a href="//questions.house-painting-info.com/changing-color-of-wood-windows.html">Changing color of wood windows</a> or this article – <a href="https://www.house-painting-info.com/restain-cabinets.html">Restain Cabinets for a New Look</a>.