No swap ? No way !!
Of course, now I'm pretty sure this is the cause of your trouble. Swap is optionnal, but you'll lose a lot of performance if you don't use it. It means the OS has no place to stock the data it doesn't immediately need when the RAM is full (so it must find any way to free some)... And I'd say Tournament 2003 must be one helluva RAM hungry game.
You must add AT LEAST a 256 MB partition (same size of your RAM) for Linux swap.
Proud owner of a Hercules Radeon 9800 Pro
Intel P!!!-S Tualatin 1266MHz | ASUS TUSL2-C i815EP | 512MB PC-133 | Antec True Power 380W
MSI GeForce 4 Ti4200 @ 250/515 | Creative SoundBlaster Live! | D-Link DFE-528TX 10/100
2 x Seagate Baraccuda IV 60GB ATA-100 7200 RPM HDDs | Pioneer DVD-117 16x/40x DVD-ROM
Windows 2000 Server SP2
DirectX 8.1 (4.08.01.0881) - nVidia Detonator 43.45 - 3DMark2001 : 8433
DirectX 8.1 (4.08.01.0881) - nVidia Detonator 30.82 (WHQL) - 3DMark2001 :
Slackware Linux 8.1
nVidia Linux IA32 Driver 1.0-4191