We do know what the design goals for 4e were, and adapting the game for online gaming wasn’t one of those. The main problems with 3e were the proliferation of character options - classes, races, feats, magic items, spells and prestige classes – which made balancing things enormously difficult for both the designers and DMs; and the built-in inequality between various classes, famously summed up as “linear fighter, quadratic wizard”, meaning that as they gained levels, full spellcasters left everyone else behind in both power and versatility.
WotC did a very good job fixing this in 4e, but it meant the loss of a lot of options, the boosting of martial characters like fighters, and the reduction in power of wizards, druids, clerics and such. The end result was a really mechanically sound game, as I mentioned, and one that was far easier to DM, especially at higher levels, but it did lose a lot of atmospheric legacy stuff and the freewheeling character-building metagame aspects of 3e that appealed to a lot of 3e fans.
5e D&D does a pretty good job at presenting a version of the game with a more “traditional” feel. While it’s not as mechanically solid or well-balanced (IMO), it still fixes 3e’s most glaring problems like the piling up of bonuses from different sources (such as buff spells and magic items), keeps spellcasters from completely overshadowing other classes, and makes fighters actually very good at fighting things, even if they can be bit lacking when they can’t solve problems with a sword.
(Why is the “video game adaptation” accusation wrong? Because in a video game you could have the computer handle all the myriad options, keep track of spell durations, areas of effect, and the overlapping bonuses from different sources, and all the rest that made high-level 3e so slow and cumbersome. In the campaigns I played that reached high levels, the players of spellcasters used Excel sheets for their characters, to keep track of spell slots, bonuses, and so on.)