Alexis is quite right. It is quite impossible for passive optics, like binoculars to concentrate or amplify light. The increased magnification increases both apparent acuity and contrast threshold improving target visibility.
The Twilight Factor is derived from the work of two Zeiss scientists, Köhler and Leinhos, published in 1955. They studied binocular performance in low light as determined by apparent visual acuity. The simplified formula only applies to quite an narrow span of target luminance (which roughly equates to moonlight) and doesn't allow for a limiting exit pupil.