I've never heard a more damning indictment of the battlemat-centric mode of combat.
But the counterpoint is that, without the battlemat, you instead have some players spending 2 minutes asking the DM to better describe where everyone in the room is, if they are close enough to attack, or move behind cover, etc. Even if the DM just described all the same things on the last player's turn.
Thing is, it will often be the same player in each example. Some player's are more easily distracted than others. I don't think the majority of battle-mat combats involve players who literally don't remember which mini belongs to them - nor do the majority of sketch map combats or DM description combats involve constant confusion of details.
But both have that potential, and the confusion usually arises based on specific players, not the system being used.
The actual comment itself, if you ignore the battlemap itself, is a good one. If you want a ten minute combat, you either need
instantaneous player turns, or very, very few rounds.
How long does a player take to do their thing? Even if playing quickly, I'd imagine it takes 1 to 2 minutes - giving them a chance to describe what they are doing cinematically, mention the specific mechanical attack, roll the dice, add up the numbers, and then have the DM tally the results. Not even counting occasional slowdowns for quick tactics questions, other players going on a tangent, etc.
So, you've got 5 players, and each one takes 1-2 minutes for their turn. Plus the DM, of course, who may have multiple monsters - but let's assume is a bit more efficient with them, so his turn takes 3-4 minutes.
And, of course, that is just one round of combat. Now, combat's don't need to go on forever, but I found that it takes a few rounds for it to feel like a real battle - if you just charge in and everything is over in the first swing, not sure how exciting that exchange really is. So let's assume that 3 rounds is a standard amount for a solid combat.
Assuming the minimum speed for players - 1 minute turns - and a 3 minute turn for a DM... that's a 24 minute combat.
For a ten minute combat, you'll need to either have everything over in a single round, or have player's acting so quickly as to totally remove the engagement in the game.
"Ok, Joe, your turn."
"Move to Orc 2, attack. Rolled a 17 to hit, for 9 damage. Done."
"John, go."
"Shoot arrows at Orc 5. Rolled a 13 and a 15, either hit?"
"The second."
"6 damage. Then I move behind these crates. Done."
Sure, you've sped things up to 20-30 second player turns... but is that really what you want? Do you want players to feel like taking their turn is a job to get over with as quickly as possible? Do you want combat to just be an exchange of shouted numbers?
For myself... maybe there are times when it is nice, and you want the quick and bloody skirmish that is over in 10 minutes. Keep people moving fast, have it a bloody fight over in 1-2 rounds.
For most fights, though, I want a bit more room for players to engage, and enough time for the combat to actually feel dynamic. And for that, the 20-30 minute fight is great. That, honestly, is the sweet spot I think is worth aiming for. And the 45 minute to 1 hour combat should be the rare exception for boss fights and truly cinematic encounters.