Orbital insertion burns do not have to change the current altitude, their only required role is purely about adding speed to the orbit bringing up the altitude of the orbit's periapsis (lowest point of the current orbit) from inside the atmosphere to roughly the current altitude (or above).

You should try out Kerbal Space Program you'll learn all about it. The rocket is perpendicular to the ground so the burn adds speed, and altitude on the other side of the orbit.

I haven't watched the footage yet, but if they were already at apopasis (highest point in orbit), orbital insertion would primarily raise the periapsis (lowest point) on the other side of the planet, so very little altitude change would be seen. It would be mostly an increase in velocity.

I think the mission was deliberately designed to get to just-below-orbit, have a decision point, and then proceed to orbit. So thats why it was a short burn. Because just-below-orbit is safer if anything goes wrong, they had a little pause.

edit: Also, Orbit is mostly a sideways speed thing rather than a height thing. The aim is to be "going sideways so fast that even though you are falling, you keep missing"