With 2. … e5, Black has a fully adequate alternative to the main variation 2. … d5 and can therefore vary his game. Disadvantage: After 2. … e5 he can no longer avoid a transfer to a classical open opening (if White wants to), because after 3. Nf3 we have the Scotch on the board. Now this is not the worst thing that can happen to Black in the King’s pawn openings (especially if White is not an expert on Scotch), but of course you should take a good look at Scotch before playing TDKS this way against 1.e4.
White has two tempting alternatives with 3.d5 and 3.dxe5, and indeed the d-pawn’s advance is the most frequently played continuation at master level (Megabase 2017) – in the amateur sector (Lichess) even by far the most played continuation. This is good news for the TDKS player, because in this variation the game becomes exciting and varied (and that’s what we play TDKS for). Personally, I don’t like the simple exchange to e5 the most, but as I said before, it happens less often, and of course you can also play the position with black afterwards.
After 3. d5, black transfers his knight via e7 to g6, and if white develops normally and continues to support his advanced pawn centre, e.g. with c2-c4, the Bf8 moves to b4 to possibly exchange himself for a knight on c3 to form a double pawn. The situation becomes sharper if White does not develop “normally”, but attacks the dark knight now standing on g6 with h2-h4 early on.