I love old tile and generally old tile was very well installed. However with this much grout failure I fear something is wrong with the substrate… if you are handy it’s certainly worth trying.

Looks like someone cleaned it with a strong acid, like toilet bowl cleaner, and it ate away the grout. It also looks like you have some cracks in your foundation (slab?) that are telegraphing their movement to the mud bed above. Since mud beds are usually pretty bomb proof, you might investigate the adjacent rooms for slab movement as well. If you find cracks, and movement, this is something serious to investigate further. Before you attempt to regrout.