The Benavides - Saduleto game starts with the King's Knight's Classical Variation but 4. Bc4 isn't mentioned as a good move in Burgess. You can see why, perhaps, in this game. The Kieseritzky 4. h4 prevents the Queen check.
Being a beginner, I'm not used to your notation. Does "KGA = -0.29" mean "after the King's Gambit Accepted by Black, White is 0.29 points (pawns) behind"?
What are u talking about Mal_Smith.
U just use Burgess with his 7 pages (if i quote u) as a source, about an opening which has been thoroughly analyzed for some centuries...
4.Bc4 is a major line, if u think nothing has been discovered since 1590, well...
Apologies, I wasn't very clear. I'll try again:
1) The Benavides - Saduleto game starts with the King's Knight's Classical Variation: 1. e4 e5 2. f4 exf4 3. Nf3 g5
2) The fourth move of White in the Benavides - Saduleto game is 4. Bc4
3) The move 4. Bc4 isn't mentioned by Burgess, so it may be be a major line, but not one Burgess considers.
4) Burgess prefers 4. h4 (The Kieseritzky line). Amongst other things, it prevents the Queen check.
I certainly think much has been discovered since 1590, which is why I'm using a modern text like Burgess.
Looking at the 365 database there are no "famous name" games using 4. Bc4 since the 1860s. The most popular move in the database is 4. h4.
Yes, exactly. 
IM poucin is right that 4. Bc4 is the second major line (4. h4 is the first major line). There are 248 master games in the Chess.com Explorer with statistics 41% / 11% / 47%.
This configuration with Nf3 and Bc4 is the least common successor of KGA: King's Gambit and KGA: Bishop's Gambit. 
IM poucin is right that 4. Bc4 is the second major line (4. h4 is the first major line). There are 248 master games in the Chess.com Explorer with statistics 41% / 11% / 47%.
Are these recent games? Then again, the line all the way to queen check and beyond is a named gambit, so it must indeed be a major line, "C37: King's Gambit Accepted, Cochrane gambit" 1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 g4 5. Ne5 Qh4+ 6. Kf1 f3. The stats in 321 chess aren't great for white! Queen bearing down, pawns attacking, it doesn't look good for White...
IM poucin is right that 4. Bc4 is the second major line (4. h4 is the first major line). There are 248 master games in the Chess.com Explorer with statistics 41% / 11% / 47%.
Are these recent games?
Two most recent (2015) master games:
https://www.chess.com/games/view/13836567
https://www.chess.com/games/view/13758009
Black wins both. In the first White avoids the h4 Queen check by sacrificing his Knight! In the second black doesn't go straight down the main line, but still wins...
U can find games with Nakamura or Shirov with white side after 4.Bc4, Ne5 isn't forced...
Well, I'm starting with 2 games going back to 1590. Evaluations are taken from the ChessOK database. I also used chess.com Analysis Board for approximative evaluations.
Benavides - Saduleto (1590): 1. e4 e5 2. f4 exf4 [KGA, -0.29] 3. Nf3 g5 4. Bc4 [-0.44] g4 [-0.22] 5. Ne5 [Salvio Gambit, -0.22] Qh4 6. Kf1 Nh6 7. d4 d6 [Salvio Gambit: Silberschmidt Defense: Anderssen Counterattack, -0.18] 8. Nd3 f3 9. g3 [-0.80] Qe7[-0.15] 10. Kf2 [-0.52] Bg7 11. Nf4
Polerio - Busnardo (1590): 1. e4 e5 2. f4 exf4 [KGA, -0.29] 3. Bc4 [KGA: Bishop's Gambit, -0.29] Qh4+ 4. Kf1 g5 [Bishop's Gambit: Lopez Variation, +0.07] 5. Nf3 [+0.04] Qh5 6. d4 [-0.18] d6 [+0.00] 7. h4 g4 [mistake, +1.5/+2] 8. Ng5 Nh6 9. Bxf4 [mistake, approx. +0.9] f6 10. Ne6 Bxe6 11. Bxe6 [approx. +0.8] (1-0).
Greco - NN (1620): 1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 [-0.44] Bc7 [KGA: Traditional variation, -0.37] 5. d4 [-0.44] d6 [-0.41] 6. Nc3 c6?! [+0.18] 7. h4 h6 [Philidor gambit: Lopez gambit (with Nc3 c6)] 8. hxg5 hxg5 9. Rxg8 Bxg8 10. Ne5? [approx. -2] dxe5 11. Qh5 Qf6 12. dxe5 Qg7 13. e6? [approx. -3/-3.5] Nf6?! [approx. -2.5] 14. exf7+?! [approx. -3.5] Kf8?? [at least, +7] 15. Bxf4!! Nxh5 16. Bd6#