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.. and here's my point of view of the skyscraper jump ;)
Not really a good choice of example videos :/
The insane lag at around 58 secs, the example at 2:00 that only shows an ingame monitor, and nothing else and then the REALLY bad example of a MTA race, all laggy and glitched up..
Oh well.. at least I'm in the race at 3:12 lol ([DKR]Bambooz)
That glitched up race demo was from the MTASA 1.1 Beta test server, which was totally underpowered. The player limit was set to 1337 for fun, but the server could hardly handle 75 players without people timing out. Due to the amount of noise around the beta test (annouced days before), well over 100 people ended up showing up on the server, totally bringing it to its knees. Still.. it was fun apart from the glitched up race test :)
It depends on your system how good it runs. Any ancient Pentium 4 or late Athlon XP or early Athlon 64 should be able to run it halfway decent (and systems based on that hardware are up to 8 years old by now).
However, one thing that is needed is a dedicated graphics card. It doesn't really matter too much how old it is, as pretty much all of them are multiple times faster than chipset integrated graphics "cards" found in countless laptops or low-end desktop PCs. This is especially true for Intel integrated graphics, usually called "GMA" (the intel GMA950 is an old, but still a very common one)
If you're on a laptop, there isn't really much that can be done, as these are in general not very upgrade friendly. A desktop PC however, could be upgraded as long as it's not too old (You have to take the cost of the upgrade vs. what the computer is worth into consideration)