Translation:There is neither a cat nor a horse here.
Ни uses the genitive case. Кошки and лошади are indeed plural forms, but they're in the nominative case. The plural nominative and singular genitive forms of these two words just happen to be the same. The plural genitive forms would have different forms, hence why it's singular. :)
In the tips of this lesson it is stated that the ending -а conjugates into -ы, not -и. Nevertheless the word кошка is conjugated as кошки, which is contradictory. The tips guide to use -и only when the ending is -я, or when a feminine noun ends in -ь.
Wikitionary agrees with the conjugation of this particular exercise. Maybe the tips should be revamped?
Here is what Master Russian website says:
"Exception 1: Because of the spelling rules, you should use the ending -и instead of -ы in feminine nouns ending in hard к, г, х, ж or ш. For example: девочка - девочки, книга книги." http://masterrussian.com/aa061500a.shtml
Don't know why щ and ч are omitted from the list.
And, you're right. Especially because the mobile app doesn't show any tips, it's relevant to cover the grammar multiple times in the first lessons.