He's right in that it's difficult to define sidequest - I'd consider it something that simply doesn't need to be done for game completion, though it would likely make said game completion easier (though not so much that it would be impossible to do so otherwise). My examples:
Civilization V:
Or really any Civ game, but I'm being specific for the sake of it. I don't know why. Civilization is a very open-feeling game, I believe, as there are many ways to play the game and multiple ways to win. It also has no sidequests. Therefore, I'd say that a game needs no sidequests to feel open, depending largely on the genre.
No More Heroes:
I wouldn't consider most of anything in it a sidequest - money is required to proceed with the plot, and missions provide it. One might say that you do the money to buy fun shirts and stuff, and that that isn't required for game completion, but the limited number of cash-generating missions means that you'll only get said cash by replaying them, and replaying a required "quest" doesn't make it a sidequest the second time around in my opinion. Perhaps the only sidequests are the "quests" (used loosely here) to beef yourself up or learn new moves via the gym and drunken bar guy (again, simply paying for something wouldn't make it a quest as per the aforementioned money collection process, as is the case with the beam katanas). But it's certainly a sandbox game in my mind, (not to the level of GTA and friends, though) what with the motorbike and the running down pedestrians and the finding cash and shirts in dumpsters or buried in the ground and all. But it doesn't feel too open to me.
Super Mario 64:
Tough to say. While one certainly needs stars to proceed through the game, which are obtained through the various worlds, you don't need all of them to finish the game. And repeating a star-collection process doesn't get a new star, only different star missions do, which may be in the same world you used for a minimum-star requirement. However, it's even possible to skip entire worlds to reach the star quota. So are all missions sidequests? Are none of them sidequests? Are re all of them potential sidequests depending on whether or not you undertake it for the fun of it? I'd say no, as none of it would better prepare you or improve your combat ability in any way, save for the hats, which are only used to be able to accomplish missions, rather than making it easier to do so.
Pokémon Red/Blue:
I don't know if I'd really consider anything from these games to be sidequests as per my personal definition, as the game is all about catching and battling pokémon. It's true that one could get through the game only by doing that which the plot demands, maybe by getting a Mewtwo in a trade or something, but it's really not the point of the game. It has the same issue as Super Mario 64 in that some battling needs to happen for game completion, but when and where it happens is a choice, making other battles an endeavor in side-questing, perhaps. Unlike Mario 64, however, the battles do make you more capable to complete the game. I'd definitely consider catching the three legendary birds (or in the case of Ruby/Sapphire, the three Regi's for instance) sidequests, as they involve going to a place separate from the plot path for the sole purpose of their capture. Again, it's a very open game, but with questionable sidequesting.
Final Fantasy Tactics A2:
Great example. By now I'm sure that some of you have various objections. "Really? The level are access through an overworld." I know. "It was so text heavy, the plot practically forced itself on you." I know. "The main character dresses like he's gay and looks like a girl." He certainly does. "You've only mentioned Nintendo games since Civilization." I have to, I've got little availability, and a tight schedule. "I hate that game you mentioned in this list." None of these are critiques of the games, and I'm not interested in discussing their merits as to whether or not they are good or bad, so shut up about that." But anyway, Tactics. Again, there are some missions that are plot-based and others that are very much not so. They are given to you in the same mission-getting spots, and are similar/the same in what one needs to do to complete them. Are they sidequests? Absolutely. They level you up, they have no impact on the plot (with good strategy, you could play through the game using only the main missions to level up), they provide access to other game options and loot for weapon crafting (still not required), and which ones you do and whether or not you do them is entirely up to you. The auctions are sidequests too - they improve your ability to play by enabling you to buy weapons at lower prices. The game's overworld format would feel very closed and linear, much like New Super Mario Bros Wii, but the sidequests open it up considerably.
The Legend of Zelda: Majora's Mask
The same could be said of all Zelda games (or as Yahtzee would say, all the versions of that one Zelda game made over and over, though I'd disagree because most games in one franchise follow the exact same linear format with only slight variations in plot, like the God of War games), but Majora's Mask demonstrates it best. There are four dungeons and the lead up requirements for their access (like Gerudo's fortress and whatnot). But obtaining the masks, the bottles, the heart containers, the better sword, the better quivers, and so on are all sidequests done through exploring the areas unrelated to game completion. And there's tons of it. Furthermore, the overworld is one in that allows for a lot of sidequest discovery, as traveling from place to place allows for the distractions known as sidequests to...distract you. This is the best example I can think of.
I don't know why I wrote all this. I'm sure no one will read it, especially not all of it. I must really be desperate to procrastinate.