It's actually Accusative, which in this case (masculine personal gender) is identical. Znam tamtych studentów (Accusative), Nie znam tamtych studentów (Genitive).
But if we make the students all female, and therefore not masculine-personal gender, then it will be: Znam tamte studentki (Accusative) and Nie znam tamtych studentek (Genitive).
Watch out for hover tips, they often don't include all the options (like here, I'm afraid), and those that are included are often correct only in proper context.
this one of those words I have a problem understanding being hard of hearing gluchy
I wrote "do you know these students" but it was marked wrong. Is there a difference for these and those?
Of course there is, 'these students' are standing closer to you than 'those students'.
Polish uses 'tamtych' and other forms a lot less often than English uses 'those'. We say that 'tych/tych/tamtych' = 'these/those/those'. So if Polish used 'tamtych', it really is 'those students over there' and therefore 'these' is not an option.