Hmmm...it would be interesting to hear from folks who actually used the system in action at GaryCon.
As you can see, this system has two big effects on combat. It makes on-the-fly actions (such as attempting to stop the fleeing hobgoblins) more uncertain. It also turns each round of combat into a miniature tactical scenario, with the players conferring about their goals for the round and their general plan of attack.
I think the article elides over the biggest effect on combat -- at a table where players will appreciate having each round be more of a tactical challenge, this system will drastically increase the time to run combats, as players hash out what their optimal strategies should be. With experience and DM prodding, perhaps this extra combat time can be minimized ("let's just use Maneuver E"), but I'm not seeing it.
The standard initiative system was designed as a 'stop messing around and just take your turn' system, and I can see where having players declare types of actions at the start of the round rather than waiting until the character's turn might help 'analysis paralysis', but in reality, I think the paralysis will just be relocated from the player's turn to the start of the round, and magnified if other players disagree with the chosen tactics.
The biggest hazard under this system is ending up in a situation where you cannot take a useful action. So when in doubt, roll a die to give yourself the option to move. In most cases, acting a little later in the round is a fair trade for the security of knowing you can close with a foe if you need to.
The manner in which actions are declared is generic enough so that it seems unlikely, barring some weird combination of effects, that you'd actually be deprived of a useful action in a round, and even then, it'll be because your allies took care of a threat that you expected to have to deal with, so I'd say that problem is not a big as suggested.
I think the true biggest hazard is the loss of the Ready action and the tactical options that closes -- for instance, imagine if, instead of appearing in a dungeon corridor, the monsters in the example were stationed behind a fortified portal (not unlike one found in the D-series manned by drow, as long as we're doing callbacks). Not only can the hobgoblins make ranged attacks, they can do so by moving in and out of cover at whim, making them impervious to counter-attack. Trying to 'interrupt' their action by delaying doesn't work, since doing this allows the action *before* the hobgoblins get their turn (and are thus still safely hidden behind the fortifications), and waiting until after the hobgoblins take their turn means exactly the same thing -- the creatures cannot be effectively targeted until the fortification is breached, which not every member of the party may be equally capable of attempting.
This is far from the only tactical situation in which the loss of the Ready action means that one side in an encounter is placed at an extreme disadvantage -- it would be up to the DM to identify these situations and attempt to avoid them in order to not antagonize her players too much.
Also, did anybody else notice that in round 4, Rupert was able to ready a shield and still attack, despite the rule on donning armor and shields requiring an action to do so?
Having to create a plan with your fellow players to work together and defeat your enemies means that coordination is critical. As such, you must weigh the benefits and risks of each action you might take in a round. As seen in the example above, healing in combat can easily become a risky proposition. One bad roll can be the difference between delivering a spell in time or seeing an ally fall under your enemies’ attacks.
Coordination sounds like a solid goal, but that's not really the game that the designers have put forward here -- 5th Edition D&D is more a game where any individual character likely has the power to change the entire tempo of the encounter with the right action taken at the right time, rest of the party be danged. The tables who will appreciate the option will pay for their entertainment with less actual adventuring accomplished in the same amount of table-time.
If the DM and players really want a game in which weighing "the benefits and risks of each action" are needed to mitigate the risks inherent in combat, maybe they should just be playing Hackmaster instead?
--
Pauper
In the AD&Dism of this variant, merely 'winning initiative' could also allow interruption, I suppose (though the variant spell disruption sidebar is very forgiving, as is, for that matter, not having to declare which spell you're casting beforehand). 
