You're mixing up two different things.
You've got a matte monitor. The top layer of glass has an almost-microscopic bumpy texture to it which scatters light. So instead of reflecting light like a mirror, it reflects as a dull sheen like an old car paint job. The only way to turn it glossy would be to grind and polish that bumpy layer off. In theory you could do it (check with telescope-making forums on how to grind glass). But in practice it would be cheaper just to buy a new monitor.
The anti-glare coating that was mentioned in Linus Tech Tips is an anti-reflective coating, like you can get on eyeglasses. They're a chemical coating a few hundred nm thick. When light strikes the surface, some of it reflects off, some of it passes through and reflects off the glass. The thickness is chosen so that these two reflects are half a wavelength apart and cancel each other out, thereby reducing the reflection. Glossy monitors use them (at least some of them do) to try to minimize the reflections. These can be stripped off with abrasive glass cleaners like Windex.
https://en.wikipedia.org/wiki/Anti-reflective_coating
Your monitor reduces glare by scattering reflections (reflecting in all sorts of different directions). The layer that was removed in Linus Tech Tips reduces glare by canceling out reflections.