I'm Slovak here. Although there are three genders, there are certain situations in which certain kinds of nouns undergo changes according to a finer subdivision than the 3 genders. I'm no expert on that. I don't think it necessarily amounts to separate genders. Or does it?
Let me see if I can recall an example. Okay, how about the word for horse, which is kôn, and man which is muž. This is masculine: ten kôn (that[masc] horse), ten muž (that[masc] man).
However, in the third person we have tý muži (those[masc] men) and tie koňe
(those[fem? neut?] horses)?
The demonstrative tie is the same like the feminine one, tie ženy (those[fem] women) or neuter tie deti (those children).
Even if that is a special gender difference, it does not fall along the animate versus inanimate line, because horses are clearly animate.
Inanimate objects that are masculine in the singular do fall into this: ten stôl (that[m] table), tie stoly (those[f] tables).
It might be human versus non-human. Collections of non-human male gender things are not themselves males, but neuters.
I find it strange that you are labelling ten/tie/.. as with gender. I don't know Slovak, but I'd expect it is the same as in Polish that the gender is on the subject. E.g., stôl is stół in Polish, and "męskorzeczowy", so masculine. "Ten stół" or "te stóły" -- te or ten is neither feminine nor masculine.
These demonstrative particles themselves don't have gender since they are not nouns, but they have a gender-based variety, and must pair correctly with the nouns by gender.
It's similar to la and le in French. You cannot say "Vive le France"; it has t obe "la France".
They are used as helpers in communicating the gender of a noun. If we say "ten stôl", it reaffirms that the noun is masculine. "tá stôl" is ungrammatical.
Other words are like this. E.g. interrogative wh- words: "ktorý muž?" (which man?) "ktorá žena?" (which woman?)
Let me see if I can recall an example. Okay, how about the word for horse, which is kôn, and man which is muž. This is masculine: ten kôn (that[masc] horse), ten muž (that[masc] man).
However, in the third person we have tý muži (those[masc] men) and tie koňe (those[fem? neut?] horses)?
The demonstrative tie is the same like the feminine one, tie ženy (those[fem] women) or neuter tie deti (those children).
Even if that is a special gender difference, it does not fall along the animate versus inanimate line, because horses are clearly animate.
Inanimate objects that are masculine in the singular do fall into this: ten stôl (that[m] table), tie stoly (those[f] tables).
It might be human versus non-human. Collections of non-human male gender things are not themselves males, but neuters.