Almost all color spaces (e.g. srgb or in the video world bt.1886) use a non-linear transfer function? I believe the difference is that gamma and log are different types of nonlinearities, see https://news.ycombinator.com/item?id=37843965 and see https://www.researchgate.net/figure/Linear-response-dashed-v... for an image comparing the two with "linear"
What's confusing is that many people will justify gamma encoding with the claim that visual perception is "logarithmic". I think this is misleading, because the perceptual justification is actually a power-law (Steven's Power Law) as contrasted by the opposing view that perception is logartihmic (Webner-Fechner law, see https://www.appstate.edu/~steelekm/classes/psy3203/Psychophy...). In practice I believe the actual justification for it was that it happened to match the transfer function of CRTs, and these days it's mostly kept around for compatibility, and as an optimization to avoid wasting bits (whether or not it truly fits the human model of perception).
As mentioned by https://computergraphics.stackexchange.com/questions/10315/t..., the real reason why log encoding is nice is because each stop of light gets roughly the same amount of bits. (Log encoding probably also isn't too bad a fit in terms of perception. In an alternate world where we weren't burdened by CRT baggage it'd be a replacement for the now-standard 2.2-esque power gamma).
Also the only reason why log encoded video "looks flat" is because traditional video workflows are not ICC color managed. If you properly applied the inverse transfer function (as any color managed system would automatically do) to display it on an e.g. sRGB screen, the video would appear close to what it did in real-life.