I haven't played The Missing Link yet, but I don't recall the story being negatively impacted by the missing section. It was far less obvious than something like Assassin's Creed 2 where they just flat-out tell you there's like 2 chapters of story that you have to buy.
I'm pretty excited for this. HR was one of my fav games ever and they're released the Director's Cut for like $5 on PC if you have the original and expansion... which I bought for like $7.50 total during a sale. Which is justified since I bought it originally on PS3 at full price for the collector's edition. It's a game so good that I don't mind buying it three times.