The exercises discussed by Owen Anderson in the linked article are effective.....but for some they may not bring full recovery.
There are cases where the root causes stem from having weaker glutes and/or hamstrings on the same side as the achilles injury and this is where doing the SAS mentioned in the article will concurrently address.
But if you also have weaker adductors/abductors on that same side you might find yourself still in pain (albeit reduced somewhat) after doing every one of those strengtheners for months.
Also, if you consistently run track work doing the same left turns or run on cambered surfaces mostly on the same side, you are also going to feel frustrated, because these are only going to aggravate your physical imbalances, which are probably the initial injury causes in the first place.
I have found that once you investigate and discover the root causes of your problem, working to train differently allows you to continue running while reaping the gains from the strengthening exercises.
Complete rest may not truly help in the long run because you allow the root causes to go unaddressed. Just doing more strengthening on the weaker muscles is insufficient; you need to change your technique so that you do not regain those imbalances again.
Staying off track completely will also not help in the long run because you still haven't addressed the imbalances and awkward style that curve-running develops in your physique. You need to try a more efficient curve-negotiating method that works better for you and you also need to run making right turns (clockwise) also to off-set some of the imbalances/misalignments in your body.
Go ahead and do all those exercises in the article; but remember to check if the muscles of the rest of your afflicted leg are the same size as those of your good leg. If u discover a noticeable difference, u will need to address those differences before u get full healing.