I've made a list of players with most goals in a single football game. I only count national leagues, regional leagues (either in Brazil or in the pre-national-league era), national cups, supercups and international games for club and country. Lower division games are excluded. Sorry for an image, but I couln't make such a good-looking list out of this system options. Just 7+ goalscorers are counted. I know about a few Germans from the pre-war era, but have to find more details. If you can suggest other candidates, please share them.
This list is great, I've been looking for the same info for months. One of the players you missed: Maximiliano SUSAN, 25.5.1909, Estudiantes de Buenos Aires - Lomas Athletic 18-0 (competition: 1909 Copa de Competencia Jockey Club) scored TWELVE goals. (source: http://www.rsssf.com/miscellaneous/ddd-argdet.html)
And recently, Andrej KRAMARIC scored EIGHT goals in ZMAJ Blato - Rijeka 0-11 (Croatian Cup - first round) on 9.10.2013, and Rhys GRIFFITHS scored SEVEN in Afan Lido - Port Talbot Town 2-8 (Welsh league) on 14.3.2014.
How much games you think are fixed from that list? Nonetheless, it"s impressive to score over 13 goals against American Samoa but it would never happen here in the Europe qualification. Say, Spain against Andorra or Gibraltar. Never would be the end result something like 31 - 0.
There is a Syrian player called Haytham Kejo who scored ten goals in one match in 98-99 season.. the match was in the first division of the Syrian league, and it was between Al Jihad vs Al Mayadeen and the score was 12-0 for Al Jihad.