The side notes state Hunde is “(archaic) dative singular of Hund,” in case anybody else was puzzled.
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It’s worth mentioning that “weiß um seine” is also at least dated, if not archaic.
Normally you would say “weiß von seiner”.
It’s totally relatable that this sentence would puzzle anyone. The entire sentence is archaic, not just because of using the word “Hunde” rather than simply “Hund”. Practically nobody today talks like that anymore. Most people would simply say:
“Jeder weiß, wie sehr er diesen Hund liebt.”
There’s nothing wrong with the given sentence. It’s just archaic. In fact, I like the given sentence because it makes you sound like Goethe or other sophisticated, eloquent writers 
Still, that’s not how the average German talks. Uneducated people might even make fun of you and ask you to talk “normal” if you talk like that.
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Just to confirm you, since I just re-read the book Siddhartha by Hermann Hesse, which was published in 1922, here’s a snippet of the book, containing that dated/archaic form of “Hund”:
At the inn, where travellers stay, he positioned himself by the door, without words he asked for food, without a word he accepted a piece of rice-cake. Perhaps as soon as tomorrow, he thought, I will ask no one for food any more.
Suddenly, pride flared up in him. He was no Samana any more, it was no longer becoming to him to beg. He gave the rice-cake to a dog and remained without food.
In einer Herberge, wo Reisende einkehrten, stellte er sich an die Tür, bat schweigend um Essen, nahm schweigend ein Stück Reiskuchen an. Vielleicht schon morgen, dachte er, werde ich niemand mehr um Essen bitten.
Stolz flammte plötzlich in ihm auf. Er war kein Samana mehr, nicht mehr stand es ihm an, zu betteln. Er gab den Reiskuchen einem Hunde und blieb ohne Speise.
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