Among the definitions for eingehen, Duden lists
sehr hoch verlieren.
Does this mean to lose by a lot? Why is this not
sehr viel verlieren?
Is that incorrect? For what reason?
They're different things. "Viel verlieren" is "to lose a lot", "hoch verlieren" is "to lose by a big margin", mainly used in sports. For example, you could say "Iran hat hoch gegen England verloren" about their 2:6 in the World Cup match earlier today.