First, let's look at Savage Worlds Deluxe to see what it means to be unarmed:
If one character has a melee weapon and his foe doesn't, the opponent is considered unarmed and is very likely in a world of hurt. Since he can only dodge and evade rather than parry, any armed attacker trying to hit him may add +2 to his fighting roll
They still have their melee weapon, don't they? They haven't dropped it or sheathed it. They can still use it to parry somewhat (it's a big pointy sword sticking out!). Therefore, they are still considered armed.
That said, there could be situational circumstances where having a weapon out may not count as a useable melee weapon. If the grappling is described as putting a dagger to the throat of the grappled character, then they can't use it to ward off an attack from another source, so I think that Unarmed Defender should be applied. Same as if they had a flail: they can't swing it to defend. But if they're wrapping their arms around the defender and are still holding a bastard sword in their hand, I can't see them being an Unarmed Defender because there's a giant pointy thing between them and any other melee attackers.
Clint does note that, in general, grappling is a "two-handed weapon", but that does not mean the same as being Unarmed. In fact, they still can make an armed attack if they choose, although at a -4 penalty for doing a two-handed action with one hand, as described in the One Armed Hindrance.
It should also be noted that although Grappling can inflict unarmed damage, that does not necessarily mean that the grappler is an Unarmed Defender. There are lots of situations where an armed character can inflict unarmed damage, like wielding a sword, but attacking with a kick or an offhand punch.