I believe you misinterpreted the phrase "This routine returns the "normalized" form of a linear differential equation, a differential operator list,...".
As written below it a differential operator list is not a list of odes but the list of the coefficients of the successive derivatives of the dependent variable of an ode.
As written in the DEnormal help page this list can be provided directly from the user, or derived from the ode by using convertAlg.
See the code bellow which is just a a commented version of the one given in this help page
# case of an ode
DE := 21*(-2*x^3)/(3*x^2-5*x+2)*y(x) + 42*(x^2)/(x+1)*x*(x-1)*D(y)(x) +
50*x^3/(x-1)^3*(D@@2)(y)(x) = x*sin(x);
# case of an operator list (here the operator list which corresponds to DE)
DE2 := convertAlg(DE,y(x));
In the convertAlg help page it's said that it "returns the coefficient list form for a linear ODE" (not of system of linear odes).
You can apply convertAlg and DEnormal for each ode in L this way
L := [diff(z(t), t, t)*m = 0, diff(x(t), t, t)*m - B*diff(y(t), t)*q = 0, diff(y(t), t, t)*m + B*diff(x(t), t)*q = 0] ;
V := [z(t), x(t), y(t)];
A := [seq(convertAlg(L[i], V[i]), i=1..3)];
N := DEnormal~(A, t);
and finally obtain the normal form of each ode this way
map(i -> add(N[i][j]*~(D@@(j-1))(op(0, V[i]))(t), j=1..nops(N[i])) = N[i], [$1..3]):
[ / d \
[ B |--- y(t)| q
[ d / d \ d / d \ \ dt /
[--- |--- z(t)| = 0, --- |--- x(t)| = --------------,
[ dt \ dt / dt \ dt / m
/ d \ ]
B |--- x(t)| q]
d / d \ \ dt / ]
--- |--- y(t)| = - --------------]
dt \ dt / m ]
But it's much simpler to do this
`Normal form of L`:= DEnormal~(L, t, V);