You need some clarification on how those terms work... In few words, Direct X is a software solution (API is the correct technical term) that binds hardware with it (specifically, graphic processors), so saying you have "Direct X 8.1 hardware" can be directly translated to "I have a video card from the late 2000" (GF4 4x00ti, Radeon 8500). Now, if you actually mean "I have Direct X 8.1 installed on my computer" doesn't say anything about the hardware you have.
This url:
DirectX has the installer for the latest one. If you actually have a card from the late 2000, this upgrade will give you compatibility with the software side of things in new games, but if certain games require hardware features your card doesn't have, you won't be able to play them still.
TL;DR: Click on the link to get the latest version of Direct X, but it doesn't guarantee you'll be able to play the latest games if your hardware is way too old.
Cheers!
EDIT: typos