Lots of great replies here.
First of all, that YouTube video was very informative. I am definitely experiencing a skills gap there which feels like a huge barrier to enjoyable play. I do not have the time or desire to practice all day or game all day. I have my fill after an hour or two per week.
Clearly some of these people just have mad skills, but I do suspect some cheating. It's like some of them can see through walls and "know" when I'll be coming around a corner inside a building. Also yesterday there was some guy who I swear was somehow firing like 4 weapons at once (rockets, plasma, pulse, and ??). I was definitely no match for an aerial assault like that.
I may look into getting a better mouse and practicing aiming somewhere other than multiplayer UT. I might have a hard time explaining to my wife why I need a new $60-80 mouse when I literally have a whole box of mice already. First I will try connecting a mouse directly to the PC instead of through the KVM switch. I checked out that Logitech G403 and it seems like a good option and not too flashy looking (just too bad it's not beige!). The only issue that might arise with gaming mice is that the onboard USB ports are 1.x and not USB 2.0, so I'd need to add a PCI USB 2.0 controller card. My Shuttle AK31 board being from 2001 or 2002 should definitely have integrated USB 2.0 but somehow does not.
Another note, I am using a healthy CRT display, playing at 1024x768 @ 85Hz, so the screen lag is pretty much a non-issue. FPS seems to stay in the 50-60 range. So, not great, but it's honestly better than what I had back in the 2000s. I could try dropping down to 800x600 for a few more frames per second.
XP: A64 3000+ S754 / 2GB DDR / 500GB SATA / Audigy1
2K: AXP 1700+ @ 1.61 / 1GB DDR / 120GB IDE / X800XL / Audigy 2ZS
98SE: P3 500 / 512MB SDR / 120GB IDE / V3 3000 AGP / Vortex2
95: P200 MMX / 32MB SDR / 3.2GB IDE
DOS/3.11: Acer 1120SX, 386SX-20