1.e3? - "Making no effort to control the center"
1.e3 is passive, but maybe you underestimate it. 1.e3 does make an effort to control the center--in fact, it controls d4. It's worth pointing out that 1.e4 also only controls one central square (d5). e3 opens diagonals for the queen and bishop, and the d2-e3-f2 pawn formation is a tough nut for an attacker to crack. GM Pavel Blatny has played this opening 40 times in tournaments against strong competition and scored 63%.
1...e5 - "I take the open invitation to control the center."
And which central squares do you control? None. You have simply contested White's control over the d4 square.
2.Nf3 - "White makes a late attempt at regaining the center with an attack on e5"
2...Nc6 - "Protect the e5 sector while I develop another piece."
The first two moves weren't mistakes, but both 2.Nf3? and 2...Nc6? are mistakes. 2.Nf3? allows 2...e4! when White's knight becomes very akward. 2.d4 was better.
3.d3? - "Another wasted move that still does little to nothing for White."
This does one positive thing for White--it prevents ...e4. The problem is, it blocks White's light-squared bishiop, and now White is down a tempo if he ever gets around to playing d4. Black is better now. 3.Nc3 would have also prevented e4, developed a piece, and carried none of the negatives I just mentioned.
3...d5 - "Now I dominate the center with solid control of the center squares"
Yes, now you have more space and more central control and you have won the opening phase of the game. You definitely outplayed your opponent.
This game i think demonstrates the importance of decisive opening strategy for white... although there are many different openings for white... some are much stronger than others... and squandering your first few moves can prove disasterous.