It's a rumor so... anything could happen with Half-Life 3 (or nothing at all). I have mixed feelings on the potential new route that the series would take by going more open-ended world (just assuming that it could possibly happen). If open world I fear that it would become more generic fetch quests-and-errands style, bordering on old style MMORPG recipes.
To some extent the Half-Life's story starting from Half-Life 2 almost "demands" a bigger world to explore... but on the other hand I'm not sure how fun it would be to explore an opened world Half-Life setting. In Half-Life 2 all those "larger" Highway 17 maps were bland and had little to offer outside of the atmosphere (at the time anyway, specifically within the game itself I mean, not compared to other games), and occasionally seeing some abandoned house on the side of the road with two or three zombies and a headcrab.
(SPOILERS AHEAD ((potentially))
In Episode Two there was a sense (good one, well-crafted) of urgency, to press on and move to the "rebels" headquarters, the story demanded it.
In the end, as much as I do like most sandbox style games (not all, mind you) I would think that the Half-Life series should remain mostly very much scripted and linear with the occasional (and minimal) more open-ended maps or specific locales without focusing on that type of game-play mechanic too much. Not a good idea if that would be the case. Such as forcing large areas on players for the sake of being large to excuse the presence or unnecessary exploration to progress a story that needs to keep going, rather than stopping by some abandoned house to play with the physics gun.
Maybe "some" larger maps here and there... sure ok, why not I guess, but limited to the strict minimum if need be. I'd rather see the series continuing on the working - and quite frankly necessary - linear path with well-crafted (sometimes quite complex) scripted scenes. The original Half-Life did very well with that, Half-Life 2 (vanilla) as well, Episode One was just too short and perhaps the story's actual progression was minimal (my personal complaints about that one anyway), and Episode Two I believe to this day was the epitome of Half-Life's own story-telling quality and progression (seriously, finally the G-Man being acknowledged officially in-game was a big one).
Honestly I do not see Valve doing that, and if anything it might be some larger maps due most likely to a new engine, but new engine doesn't have to mean nor to oblige a sandbox style game at all. When I think about it, this reminds me of the original Crysis, its engine blew us all away when we first saw the game in action, but the thing is the CryEngine can on paper produce huge areas in which you can make some type of a sandbox game (or map if you prefer), but ultimately Crysis was (is) a linear story-driven and quite scripted game... only with "bigger than usual" maps since the engine kinda allows it. Perhaps the "worst" case scenario (or best, depending on how you see it) is that Half-Life 3 might end up still being linear and scripted, based on its story that needs to be told and so that it needs to be story-driven, but its maps may allow some sort of sideline exploration if the player chooses to do so, but the story itself wouldn't demand the player to do it (I.E. no randomly placed NPCs around to find and accept errand-style quests from).
It's my take on the possibility, but ultimately I do not believe it's going to happen the same way most people might be envisioning it at the moment (A.K.A Half-Life turning into a full-fledged Elder Scrolls-style sandbox game).
