Are you asking if you can activate "Hand Destruction" in the TCG without both players having at least 2 cards in their hand? If so, that's not what its PSCT is telling us; both players must have 2 or more cards in their hand and Deck in order to activate
The difference between the CGs is when resolving
In the OCG, its Ruling
is that both
players must send 2 cards from their hand, then both
players draw 2 cards (or lose the Duel, if a card or effect is chained so that one or both players have less than 2 cards in their Deck when resolving "Hand Destruction"). If a card or effect is chained, such as "Effect Veiler," so that one or both players have less than 2 cards in their hand when resolving "Card Destruction," the effect resolves without doing anything since it requires both players.
In the TCG, its PSCT states that each
player sends 2 cards from their hand to the Graveyard, then draws 2 cards. This means that when "Hand Destruction" is resolving, if one player have less than 2 cards in their hand, the other player still applies the effect. The new errata for "Hand Destruction" didn't change its function in the TCG, but rather clarified it. Previously, you can interpret the text several different ways -- it was ambiguous; for example, you can interpret it as if only one player sent cards to the Graveyard, "each player draws 2 cards," so the player who didn't send any cards in their hand to the Graveyard will still draw.
Now I'm not exactly sure which CG's "Hand Destruction" YGOPro is currently using, but regardless, the bottom line is that the errata changed nothing. You still need both players to have 2 or more cards in their hand and Decks in order to activate "Hand Destruction"; in the OCG, the effect needs both players to send in order for it to apply at all; in the TCG, the effect can be applied as long as one player is able to send 2 cards from their hand.
Edited by user
| Reason: Not specified