"My dog is bigger than yours."
Translation:Mein Hund ist größer als deiner.
German like English, distinguishes between possessive determiners / possessive adjectives on the one hand and possessive pronouns on the other hand.
For example, in English, we have "your dog" (possessive determiner "your") but "yours" (possessive pronoun).
Possessive determiners stand before a noun, but possessive pronouns (like other pronouns) stand by themselves, in place of a noun.
In German, possessive determiners and possessive pronouns mostly have the same endings, but in the nominative singular, the possessive determiners have no endings for masculine or neuter nouns while the possessive pronouns do.
Thus Dies ist mein Hund und das ist deiner (masculine) and Dies ist mein Pferd und das ist deins (neuter). Compare English "This is my dog and that is yours". (I wonder whether the -s on "yours" is related to the -s on deins.)
Because this is the comparative form of groß and not just a declined form of the positive: https://www.cactus2000.de/deutsch/adject/showadj_en.php?adj=gross&mode=1
Google has "deins" at the end of the sentence. Is this a correct genitive usage?
No; deins is not genitive. It's nominative or accusative for neuter nouns, e.g. Mein Pferd ist größer als deins (= als dein Pferd). "My horse is bigger than yours (= than your horse)."
But Hund is masculine, so it has to be deiner.
For a feminine nouns such as Katze, it would be deine.
Duden, under https://www.duden.de/rechtschreibung/dein_Possessivpronomen 1b, calls deines "gehoben" ("elevated" language).
Which matches my feeling; using deines feels very "posh" and deins is the usual way I would expect to hear it.
Why was "Mein Hund ist größer als eurer" marked incorrect?
I'll bet you 50 lingots that that was not the sentence that was marked incorrect.
Mein Hund ist größer als eurer is one of the accepted translations.
If you can show me a screenshot showing that that sentence is rejected, I'll give you 50 lingots. (Upload it to a website somewhere such as imgur or postimage and put the URL of the image in a comment here.)