Most chess-playing computer programs have a "book" in the software that lays out opening lines for the program to play. This saves on computing time - i.e. why analyze the "best" 6 or 8 opening moves, game after game - and makes sure that the program gets off to a reasonable start. It can include the latest preferences of super-Grandmasters, or the favorite moves of the programmer.
Given that the Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+) is not likely to be deemed "best" play for White by the analysis of any competent computer, any time the opening is played by a program, it is likely that the Jerome has been included in the opening "book".
A computer program dedicated to playing the Jerome Gambit - like Brause, focused on the Halloween Gambit, mentioned in an earlier post - would be a gift to the Jerome Gambit Gemeinde; but, alas, such a thing apparently does not (yet) exist.
I cross-checked the list of 130 or so computer "players" at the Free Internet Chess Server with the roughly 55,000 games in The Database. I found 9 additional (see Part 1 and Part 2 for the games of GriffySr and GriffyJr) games showing a variety of Jeromes - the Jerome Gambit proper, the Abraham Jerome Gambit, the Blackburne Shilling Jerome Gambit, and the Semi-Italian Jerome Gambit.
Gamin - mscp
blitz, FICS, 2001
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.d3 Nge7 6.Bg5 Kg8 7.Nc3 h6 8.Bxe7 Qxe7 9.Nd5 Qd8 10.c3 a5 11.Qb3 a4 12.Qc4 a3 13.Nxc7+ d5 14.exd5 axb2 15.dxc6+ Kh7 16.Rb1 Qxc7 17.Qxc5 e4 18.dxe4 Rxa2 19.Qc4 Ra6 20.Qd3 Qxc6 21.Qc2 Kg8 22.Nd2 Ra2 23.Rxb2 Ra1+ 24.Rb1 Rxb1+ 25.Nxb1 Qa6 26.e5 g6 27Nd2 Rh7 28.Ne4 Qa1+ 29.Qd1 Qxd1+ 30.Kxd1 Rh8 31.Nd6 Bd7 32.Ke2 Rh7 33.Kd3 Bc6 34.f3 Rd7 35.Ra1 b6 36.Kd4 b5 37.Kc5 Bb7 38.Ra7 Bc6 39.Ra6 Rxd6 40.Kxd6 Bb7 41.Ra7 Bxf3 42.gxf3 g5 43.e6 b4 44.cxb4 g4 45.e7 Kf7 46.fxg4 h5 47.gxh5 Kf6 48.e8=Q Kg5 49.Qg6+ Kf4 50.Re7 Kf3 51.Qg3 checkmate
Gamin - JumpNMustangII
lightning, FICS, 2001
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.Nxe5+ Nxe5 6.d4 Bb4+ 7.c3 Qh4 8.O-O Nc6 9.Qf3+ Qf6 10.Qh5+ g6 11.Qd5+ Qe6 12.Qxe6+ dxe6 13.cxb4 Nxd4 14.Na3 Ne2+ 15.Kh1 Nf6 16.Re1 Nxc1 17.Raxc1 c6 18.Nc4 Rd8 19.e5 Nd5 20.Nd6+ Ke7 21.Re4 a5 22.b5 cxb5 23.Rh4 h5 24.Nxb5 Nb4 25.Nd6 Bd7 26.Nxb7 Rdc8 27.Rxc8 Rxc8 28.h3 Rc2 29.Nxa5 Rxb2 30.a3 Nd3 31.f4 Ne1 32.Nc4 Rxg2 33.Nb6 Rc2 34.Nd5+ exd5 35.f5 Nf3 White resignedlightning, FICS, 2001
SiliconC - cesrmathurine
standard, FICS, 2005
standard, FICS, 2005
1.Nf3 Nc6 2.e4 e5 3.Bc4 h6 4.d4 exd4 5.Nxd4 Bc5 6.Bxf7+ Kxf7 7.Qh5+ g6 8.Qxc5 Nxd4 9.Qxd4 Qf6 10.Qd3 d6 11.Qc4+ Be6 12.Qxc7+ Ne7 13.O-O Rac8 14.Qxb7 Rxc2 15.Qxa7 Rhc8 16.Qe3 Bc4 17.Re1 Bd3 18.Na3 Bxe4 19.Qxe4 Qxf2+ 20.Kh1 Re2 21.Qxe2 Qxe2 22.Rxe2 Nf5 23.g4 Nd4 24.Re4 Nf3 25.Rf4+ Kg7 26.Rxf3 Black resigned
fjjvh - nicoben
blitz, FICS, 2006
1.e4 e5 2.Bc4 Bc5 3.Bxf7+ Kxf7 4.Qf3+ Nf6 5.Qb3+ Kf8 6.Qf7+ Kxf7 7.Nf3 Ng4 8.Nxe5+ Nxe5 9.f4 Ng4 10.h3 Nf6 11.e5 Ne4 12.e6+ Kxe6 13.f5+ Kxf5 14.Rf1+ Kg5 15.d3+ Kg6 16.Rf6+ Kxf6 17.Bg5+ Kxg5 18.h4+ Kxh4 19.g3+ Kxg3 20.dxe4 Qe8 21.a4 Qxe4+ 22.Kf1 Qxc2 23.Ra3+ Bxa3 24.Nxa3 Qxb2 25.Nc4 Qg2+ 26.Ke1 Qf2+ 27.Kd1 Qf1+ 28.Kd2 Qxc4 29.a5 b6 30.Ke3 bxa5 31.Kd2 Re8 32.Kd1 Kf2 33.Kd2 Re2+ 34.Kd1 Qc2 checkmate
Gamin - cccolts
blitz, FICS, 2007
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.d3 h6 6.O-O Nf6 7.Be3 Bxe3 8fxe3 Rf8 9.c3 Kg8 10.Nbd2 d6 11.d4 Bg4 12.Qb3+ Kh8 13.Qxb7 Qd7 14.Qa6 Bxf3 15.Rxf3 Rab8 16.Rb1 Rb6 17.Qa3 Re8 18.d5 Ne7 19.Qxa7 Reb8 20.b3 Ng6 21.Rbf1 Kh7 22.Rg3 R8b7 23.Qa5 Rb5 24.Qa4 R5b6 25.Qxd7 Nxd7 26.a3 Ra6 27.Rf7 Nc5 28.b4 Nd3 29.Nc4 Ne1 30.a4 Rba7 31.a5 Kg8 32.Rf1 Nc2 33.Rxg6 Black resigned
lightning, FICS, 2009
1.e4 Nc6 2.Nf3 e5 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.O-O Nf6 6.d3 Rf8 7.Be3 Bxe3 8.fxe3 d5 9.exd5 Nxd5 10.Nxe5+ Kg8 11.Rxf8+ Qxf8 12.Nxc6 Qc5 13.Qe2 bxc6 14.d4 Bg4 15.dxc5 Bxe2 16.Nd2 Bh5 17.e4 Nb4 18.c3 Nd3 19.b4 a5 20.a4 axb4 21.cxb4 Nxb4 22.a5 Nd3 23.a6 Ra7 24.Nb3 Bf7 25.Rd1 Bxb3 26.Rxd3 Be6 27.Rd8+ Kf7 28.Rb8 Rxa6 29.Rb7 Ke7 30.Rxc7+ Bd7 31.Kf2 Ra5 32.g3 Rxc5 33.Ke3 Ra5 34.Rb7 Ra2 35.h3 Ra3+ 36.Kf4 c5 37.h4 c4 38.Ke5 Rd3 39.Ra7 c3 40.Rc7 Kd8 41.Rc4 Bb5 42.Rc5 Ba4 43.Ke6 c2 44.Kf7 Rd7+ 45.Ke6 Rc7 46.Rxc2 Bxc2 47.Kd5 Rd7+ 48.Ke5 Re7+ 49.Kf4 Rxe4+ 50.Kf3 Ke7 51.Kf2 Kf6 52.Kg2 Kf5 53.Kf2 Kg4 54.Kg2 Re2+ 55.Kf1 Bd3 56.h5 Kxg3 57.h6 Re3+ 58.Kg1 Re1 checkmate
BlackDemon - abhaysonu
blitz, FICS, 2009
1. e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.Nc3 Nf6 6.O-O Re8 7.d3 Kg8 8Bg5 Be7 9.Bxf6 Bxf6 10.Nd5 d6 11.h3 Ne7 12.Nxf6+ gxf6 13.d4 Ng6 14.c3 Kh8 15.Ne1 Rg8 16.Qf3 Qe7 17.Kh1 Qg7 18.Rg1 Nh4 19.Qd3 Bxh3 20.Qxh3 Ng6 21.Nd3 Nf4 22.Nxf4 exf4 23.Rae1 Rae8 24.Kh2 Qg6 25.Qh4 f3 26.gxf3 Qf7 27.Rxg8+ Rxg8 28.Rg1 Rxg1 29.Kxg1 Qxa2 30.Qxf6+ Kg8 31.Qd8+ Kf7 32.Qxc7+ Kg6 33.Qxd6+ Kh5 34.Qd5+ Kh6 35.Qxa2 Black resigned
callipygian - vuhb
blitz, FICS, 2009
1.e4 e5 2.Bc4 Bc5 3.Bxf7+ Kxf7 4.Qh5+ g6 5.Qxe5 Bxf2+ 6.Kxf2 Qf6+ 7.Nf3 d6 8.Qg5 Nc6 9.Rf1 Qxg5 10.Nxg5+ Kg7 11.d3 Nd4 12.Na3 Nf6 13.c3 Ne6 14.Nb5 Ne8 15.Kg3 Rf8 16.Nxe6+ Bxe6 17.Bh6+ Kxh6 18.Rxf8 Kg7 19.Rf3 c6 20.Nd4 Bg8 21.a4 Nf6 22.a5 c5 23.Nb5 c4 24.Nxd6 cxd3 25.Rxd3 Be6 26.Kf4 Rf8 27.Re1 Nd7+ 28.Kg3 Ne5 29.Rdd1 b6 30.axb6 axb6 31.Nb5 h5 32.Nc7 Bg4 33.Rd5 Rf7 34.Ne8+ Black resigned
LittleBugger - Nicolayevich
blitz, FICS, 2012
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nd4 4.Bxf7+ Kxf7 5.Nxe5+ Ke7 6.Nc3 d6 7.Nd5+ Ke8 8.Qh5+ g6 9.Nxg6 Nxc2+ 10.Kd1 Nxa1 11.Ne5 checkmate