Like I said, later in the study they talk about the removal and then re-addition of the adamantane group. Look at quotes #5 and #7. It's still in the context of anti-viral activity, which is what your quote discusses.
The underlined portions of the quotes I posted, and especially the parts in read clearly show that the authors of that study consider the adamantane group to be a pharmacophore, and in some cases a required one for observed effects. Quotes #8, #10, #11, #12, #14, and even #18, and #19 are such examples.
But if the adamantane group is responsible for the anti-viral activity of amantadine, then how come 'Replacing the amino group in amantadine with other functional groups like –OH, –SH, –CN, –CO2H, –Cl, or –Br gave inactive compounds.'
In this case the adamantane group is still there, but the amino group is not, and the compounds are inactive.