Part of the Microsoft Media Center requirements is the card be hardware based. So yes you need a hardware card.
The listed card does meet that requirement, however its dual tuners are one analog(can be connected to a set top box or just regular cable) and one digital for over the air tv(Antenna). In large cities there are lots of over the air digital channels available. Some cable providers do provide channels the digital tuner will pick up, but its rare. The HVR will only control one set top box, since they expect the digital tuner to be pulling from over the air channels.
http://www.hauppauge.com/pages/products/data_hvr1600.html
You have not mentioned the source you want to record from. If its just SD TV, something like a PVR 500 will do it(but as said you need 2 set top boxes come 2009 or even now depending on you cable provider[if you satellite you need 2 boxes for sure]), but this card will never do HD.
PVR 500
http://www.hauppauge.com/pages/products/data_pvr500mce.html
The TMPGEnc or DivX Author software are just suggestions to compress your video to save space(A move takes about 7 gigs of space in Mpeg2 and only 1-1.4 in DivX), they are in no way needed to watch it. in fact Vista MCE will do the playback for you.
I have my set top box connected to the computer for recording(i do not watch while it records on the computer, i play games
or just watch on the tv)
Nvidia used to have a line of TV cards called Nvidia Personal Cinema, but they are not made any more as far as i know.
I will try to clear up why the suggestion to use a DVR from your cable company.
to record TV I have
Set top box
Computer(with TV card and video card with TV out)
TV(you can use your computer screen, but its higher resolution will show every flaw in the tv picture)
Ir receiver(more the MCE remote)
Ir blaster(plus into the Ir receiver to allow the computer to change the channels on the set top box)
Remote
With it all setup its like this
imagine this 2 times even without the tv it can get messy
Its fairly messy when for 10$ a month or what ever they charge you can have a set top box with a hard drive built in for recording. The reason i use the computer is so i can keep things. on a set top box it has to stay on the box, but TiVo has a service to get your tv off the box(never used it tho.)
From the cable company you have
Box
TV
Remote
I hope this clears it up a bit. I will still use my computer because i have always had it setup that way, but depending on your needs a DVR may work just as well.