the D&D Adventures engine they are still using for board games isn't exactly 4E in full: but it is a "Basic" version of it. The gameplay part is the same
No.
4e is a RPG. The fiction matters to the resolution. Wrath of Arshadalon et al are board games, which is to say the fiction is merely an overlay of flavour, like Monopoly or M:tG, and doesn't matter to resolution.
The gameplay is very much not the same.
This difference in gameplay can also be seen in differences in resolution and scenario-design procedures. The starting points for elaborating those resolution differences would be that the boardgame has no skill challenge system, no p 42, no section on damaging objects (which is a key adjunct to p 42 in the 4e DMG), and uses purely algorithmic processes for determining monster/NPC actions. For scenario-design procedures, one would start with the absence from the boardgames of the "quest" approach to adventure design and of a whole host of informal devices for player flag-flying (eg race, class, background, theme, paragon path, epic destiny).
It gives the same tools folks have been using to do TotM for decades; the same tools we used in 3.x to do it that way.
It seems to me that those tools are nothing but movement rates, ranges and AoEs. 4e has them too.
AD&D has very little forced movement, and (subject to [MENTION=55664]ABDULa[/MENTION]lharazed's caveats that there is no single AD&D, given its incoherence/incompleteness) once melee is joined position doesn't really matter (of course flanking and rear attacks matter, because they negate various bonuses to AC, but these are worked out based on number of foes vs a single figure, not via tracking individual movement and facing round-by-round). Hence ToTM is not too hard to manage in my experience. (For melee, that is; for AoE spells it generates all the usual arguments about who is where - long before 13A introduced technical rules for rolling dice to see how many targets you get, I remember assigning probabilities to various targets being in our out of the AoE and then rolling to see how it panned out.)
(In post 122 [MENTION=82106]AbdulAlhazred[/MENTION] makes some similar obvservations about the contrast with AD&D.)
But 5e's action economy and resolution mechanics track individual figure position just the same as 3E and 4e, and it seems to have quite a bit of forced movement. The only difference I can see from 4e is that it expresses everuthing in multiples of 5' rather than squares - if
that is what counts as ToTM support (qv post 124), though, then I'm a bit surprised! Is multiplying by 5 all that stands between 4e's rulebooks and legions of TotM 4e-ers?