This is all a rumor, and the logo above is not real as well. Ex-Battlefield 3 lead designer, David Goldfarb, had a rather interesting conversation with Notch on Twitter, as seen below during Game Developers Conference (GDC) 2013. Notch, as you might have known, is the creator of Minecraft.
To me, it certainly looks like Valve teased Half-Life 3 behind closed doors to a small group of developers. The company never denied nor confirm the game’s existence all these years, and hopefully some info can be made public soon.