Drills: Help me understand why this is the best move

(I don't know if I should be posting this here, or in Game Analysis.)

I'm doing one of the Drills for beginners (Puzzles > Practice (Drills) > Drills > Attacking), the Phildor Defense: Pressing a Space Advantage. After playing through it a few times, seeing what moves are recommended and which ones are considered mistakes or blunders, I reset and get to this position:

The computer says that 4. Nxe7+ is the best move, but I can't figure out why since Black's rook on e8 will just take my knight. But I make the move anyway to see what happens. On Black's turn, the king retreats to h8. The rook doesn't take my knight. Whu...? The e8 square is being attacked by my queen on b5 and no one else; e8 is being defended by Black's queen on c8 and knight on f6, and after the rook takes my knight, that rook is now defending e8, as well. If I go 5. Qe8+, I'll just loose my queen. The rook taking my knight seems like an easy grab, but it appears it's not.

So what gives? Why is 4. Nxe7+ the best move, and why doesn't Black respond with 4. ...Rxe7? Am I missing something obvious? Thx.

EDIT: Sorry, I inserted the game wrong. My knight was on f5 and took Black's bishop on e7. Black's king was on g8 and retreated to h8.

if 4. Rxe7, then 5. Bxf6 gxf6, you play Nd5 hitting both the pawn and the rook.

If the rook goes back to e8, you can take the pawn on f6 and fork the king and the rook. The same thing happens with Rd7 and if he plays Rc7 then you just take rook with the same knight.

So after Nd5 black has to play Re6 to defend the pawn but after that you play f4 attacking the knight on e5 so after the black plays Nd7, you attack the rook with f5 and after rook moves out of the way, you have a tactic where you can take the knight on d7 sacrificing the queen and after Qxd7, you can play Nxf6 forking the King and Queen and after Kh8, you play Nxd7 and you are up by a full knight and a pawn.

I hope this helped you understand

If RxN, then BxNf6, gxf6 opening file to the K, Nd5 threatens NxR, gaining the exchange; if Re6, it blocks c8-b3 diagonal, rendering Q & Rs underdeveloped. White has a rook lift and Q moves to kingside to attack black’s open K.

As the position is now, BxN, then Nc3-d5, white has great control and Black’s K is still exposed.

Just my thoughts on a quick review

Talliholic— I did not see your post when I started my reply.  Good to know I was on the right track

Wow! Thank you, both. That was what I was missing. I'm still trying to wrap my mind around positional advantage and disadvantage, and I hadn't thought to try to play it out that way (it didn't occur to me that I could play both sides in the drills). Seriously, @talliholic and @CenterMass51075, that made perfect sense. I feel like I'm a step ahead now! I really appreciate the help.

Ok