the acer aspire one has the same intel graphics chip that most other first gen atom
processors came with (depending upon which acer aspire one as there were a few).
http://en.wikipedia.org/wiki/Acer_Aspire_Onethis falls under the same 810 chipset that most intel chipsets fall under, and it was built into one of the support chips.
so same as samsung NC10, eePC atom version and many miniitx boards.
DirectX is a microsoft graphics API, it does not exist in linux, and things written to use it, cant run properly in linux.
(exception:some windows apps and games can run under wine, and they may make use of DirectX within wine, im not really sure)
but if you have aspirations to play games on an acer aspire one with an atom chip, via wine, I would suggest investing in something a bit more capable.
I have an NC10, that used to be my mageia 1 portable. equipped with an SSD and 2 gig of ram, its quite usable as a 2D portable internet, email, etc type of use. much like a chromebook.
as mageia goes up in revs the requirements slowly outgrow this type of device, hence why they are not readily sold any more.
they were never realisticly capable of running windows 7, on the atom versions.
regards peter