Very interesting, and on the face of it, it is very good news. The only thing to keep in mind is that. Even though a particular chain may be using meat that is truly Halal today, there is no guarantee that they might switch to some other meat which would not comply with the Halal standards we all agree with here. Them using Halal eat today could be a coincidence not that they really care about Halal standards. So the actual long term solution is that there be reliable Halal certifying bodies in Saudi that ensure this.
Secondly, while the focus is mostly on chicken being hand -slaughtered, one must not forget that in the case of beef, there is the question of vertical and horizontal cut. And the vertical cut is not considered permissible according to the opinion of those Ulama who we tend to follow in these matters. Did hear someone say (probably on this forum) that goat/lamb are the safest choices. Allah SWT knows best.
Saudi supermarkets sell meat that is not even labelled Halal at all (let alone getting into the Halal technicalities), i.e. it is the same meat brands that are sold in supermarkets in the United States. So as a whole you can understand how lax their approach is to Halal food.