Intel 810E Has PPGA socket . No your Pentium 3 is not Supported on 865GF Board.
If you want to upgrade or not throughly depends how much time you want to devote to gaming. If you are mild and casual gamer just half hour in 2 days or so then get PCI Based Geforce Mx 4 card at around 3k.
But if u intend seriously enter gaming scenario then upgrade is the only path for you, A New ATX cabinet , CPU Ram n Proccy is what you will need. OF course the Graphic card comes too.
So its up to you . Want to be casual gamer , a medicore or Hardcore Gamer ?
Merry Christmas !!