Isn't the velocity in an orbit always tangential, not radial and tangential? In this video the person resolves the momentum vector into two components, tangential and radial. But isn't the velocity at every point on the orbit tangential?
 A: I think it's just a misunderstanding!

But the velocity at every point on the orbit must be tangential right?

Yes,it is and that's why the actual momentum vector is tangential to the ellipse

this person resolves the momentum vector into two components , tangential and radial

And yes he did.But,you should notice that he called one radial and the other perpendicular i.e  the resolution is done according to the line joining the object's(planet's) location and sun and the object has radial velocity because radial velocity is defined as the component of the object's velocity that points in the direction of the radius connecting the object and the point.
And if you look at what you are calling as tangential velocity you would notice that this component, i.e perpendicular to line joining planet and sun, isn't tangential to the ellipse.It's just perpendicular to the line joining the planet and the ellipse.
Conclusion: The planet always has velocity tangential to the ellipse and the velocity perpendicular to the line joining planet and object isn't tangential to the ellipse at all instants.
Note:
Although in your question you particularly ask about momentum I just used the term velocity rather than momentum because I think it is easier to understand this way.
If you need momentum at any instant just multiply total velocity with mass(p=mv)
References:
https://en.wikipedia.org/wiki/Radial_velocity
https://www.youtube.com/watch?v=Pa3Of_3vpRc
