The reason why the rule 104.3c is worded this way is because some effects instruct the player to do something after they have drawn the cards which might change the outcome of the game. It is a pretty rare scenario, but consider these:

You cast Blast of Genius with less than 3 cards in your library. You still draw as many cards as you can, then discard a card and deal damage equal to the discarded card's CMC. If your chosen target was your opponent and the damage was enough to bring them to 0 or less life, the next time state based actions are checked (immediately after Blast of Genius finishes resolving), the game will find that both players have lost the game, ending the game in a draw.

You have less than 7 cards in your library and activate Jace, Wielder of Mysteries -8 abiity while he has exactly 8 loyalty, which means that he will be put into the graveyard before the ability resolves, so his static ability will not apply. You will draw as many cards as you can, and then, as part of the ability, win the game. If for some reason, you do not win the game (e.g. the opponent cast Angel's Grace in response), you will lose the game immediately after the ability finishes resolving because you attempted to draw from an empty library.

Rule 104.3c is only relevant when a player attempts to draw multiple cards at once. The scenario described in the question is slightly different, because Howling Mine places separate "draw 1" triggers on the stack. This means that the opponent will get an opportunity to respond to each Mine separately. For example, if they had 3 mines out and 3 cards in the library, all Lightning Bolt, they will be able to cast all the bolts before losing to the third mine trigger. Or if one of the cards was a Twiddle, they will get an opportunity to tap the last mine, negating the draw and continuing to their main phase.

The reason why the rule 104.3c is worded this way is because some effects instruct the player to do something after they have drawn the cards which might change the outcome of the game. It is a pretty rare scenario, but consider these:

You cast Blast of Genius with less than 3 cards in your library. You still draw as many cards as you can, then discard a card and deal damage equal to the discarded card's CMC. If your chosen target was your opponent and the damage was enough to bring them to 0 or less life, the next time state based actions are checked (immediately after Blast of Genius finishes resolving), the game will find that both players have lost the game, ending the game in a draw.

You have less than 7 cards in your library and activate Jace, Wielder of Mysteries -8 abiity while he has exactly 8 loyalty, which means that he will be put into the graveyard before the ability resolves, so his static ability will not apply. You will draw as many cards as you can, and then, as part of the ability, win the game. If for some reason, you do not win the game (e.g. the opponent cast Angel's Grace in response), you will lose the game immediately after the ability finishes resolving because you attempted to draw from an empty library.

The first half of rule 104.3c is mostly relevant when a player attempts to draw multiple cards at once. Howling Mine places separate "draw 1" triggers on the stack. This means that the opponent will get an opportunity to respond to each Mine separately. For example, if they had 3 mines out and 3 cards in the library, all Lightning Bolt, they will be able to cast all the bolts before losing to the third mine trigger. Or if one of the cards was a Twiddle, they will get an opportunity to tap the last mine, negating the draw and continuing to their main phase.

The reason why the rules are worded this way is because some effects instruct the player to do something after they have drawn the cards which might change the outcome of the game. It is a pretty rare scenario, but consider these:

You cast Blast of Genius with less than 3 cards in your library. You still draw as many cards as you can, then discard a card and deal damage equal to the discarded card's CMC. If your chosen target was your opponent and the damage was enough to bring them to 0 or less life, the next time state based actions are checked (immediately after Blast of Genius finishes resolving), the game will find that both players have lost the game, ending the game in a draw.

You have less than 7 cards in your library and activate Jace, Wielder of Mysteries -8 abiity while he has exactly 8 loyalty, which means that he will be put into the graveyard before the ability resolves, so his static ability will not apply. You will draw as many cards as you can, and then, as part of the ability, win the game. If for some reason, you do not win the game (e.g. the opponent cast Angel's Grace in response), you will lose the game immediately after the ability finishes resolving because you attemted to draw from an empty library.

Rule 104.3c is only relevant when a player attempts to draw multiple cards at once. The scenario described in the question is slightly different, because Howling Mine places separate "draw 1" triggers on the stack. This means that the opponent will get an opportunity to respond to each Mine separately. For example, if they had 3 mines out and 3 cards in the library, all Lightning Bolt, they will be able to cast all the bolts before losing to the third mine trigger. Or if one of the cards was a Twiddle, they will get an opportunity to tap the last mine, negating the draw and continuing to their main phase.

The reason why the rule 104.3c is worded this way is because some effects instruct the player to do something after they have drawn the cards which might change the outcome of the game. It is a pretty rare scenario, but consider these:

You cast Blast of Genius with less than 3 cards in your library. You still draw as many cards as you can, then discard a card and deal damage equal to the discarded card's CMC. If your chosen target was your opponent and the damage was enough to bring them to 0 or less life, the next time state based actions are checked (immediately after Blast of Genius finishes resolving), the game will find that both players have lost the game, ending the game in a draw.

You have less than 7 cards in your library and activate Jace, Wielder of Mysteries -8 abiity while he has exactly 8 loyalty, which means that he will be put into the graveyard before the ability resolves, so his static ability will not apply. You will draw as many cards as you can, and then, as part of the ability, win the game. If for some reason, you do not win the game (e.g. the opponent cast Angel's Grace in response), you will lose the game immediately after the ability finishes resolving because you attempted to draw from an empty library.

Rule 104.3c is only relevant when a player attempts to draw multiple cards at once. The scenario described in the question is slightly different, because Howling Mine places separate "draw 1" triggers on the stack. This means that the opponent will get an opportunity to respond to each Mine separately. For example, if they had 3 mines out and 3 cards in the library, all Lightning Bolt, they will be able to cast all the bolts before losing to the third mine trigger. Or if one of the cards was a Twiddle, they will get an opportunity to tap the last mine, negating the draw and continuing to their main phase.