In glycolysis, during oxidation electrons are removed by -

Glycolysis breaks one glucose into two molecules of pyruvic acid in the cytoplasm.
The only oxidation step is the conversion of glyceraldehyde-3-phosphate (PGAL) into 1,3-bisphosphoglycerate.
In this step, two electrons and a proton (a hydride ion) are removed from PGAL and accepted by the coenzyme $NAD^+$, which is reduced to $NADH + H^+$:
$PGAL + NAD^+ + P_i \rightarrow 1,3\text{-}BPGA + NADH + H^+$
Glyceraldehyde-3-phosphate is the compound being oxidised, not the electron acceptor. Molecular oxygen is not used in glycolysis (it is the final acceptor only in the electron transport chain).
So in glycolysis electrons are removed by $NAD^+$.