Serious shenanigans required. Earth is mostly a very dense, hot liquid, and even a cooled-off, solid body with Earth's mass will end up as a spheroid due to gravity's effects.
(This is due to the Inverse-Square Law--the force exerted by gravity is inversely proportional to the square of the distance from the center of the mass exerting the gravitational force. So matter experiences equal amounts of gravity at all points on a sphere a given distance from the center of the mass. Therefore matter with sufficient mass for a nontrivial gravitational field which is then shaped into spindle isn't going to remain spindle-shaped because a spindle doesn't distribute the mass evenly across the sphere-shaped field. It's not at at an equilibrium, gravitationally. The mass at the pointy ends, or any other matter caught in the gravitational field, will fall toward the middle until the force of gravity is equalized across the surface, which is to say, when it's a spheroid.)
A spindle-shaped planet of earth's mass at equilibrium would require continually operating gravity manipulation. The shape of the gravitational field would have to be altered into and maintained as a spindle.
Moreover, the spinning, liquid, spherical core of earth (mostly iron and nickel) is also important for life's existence. It creates our planetary magnetic field, which in turn prevents us all from having our DNA constantly rearranged and destroyed by solar radiation. That deadly radiation instead gets trapped by earth's magnetic field in the van Allen radiation belts. None of which is compatible with a spindle-shaped planet. (Magnetism also follows the Inverse-Square Law, as does every flux- or field-based force.)
So in order to make a spindle-shaped planet workable, the aliens have got to either alter the Inverse-Square Law, either locally or across all of physical reality, either of which seems like it would be hard to do, and would have a ton of repercussions--all planets, stars, and orbits would be spindle-shaped, for one--or they've got to locally manipulate gravity and magnetism (or just gravity, and then provide some other means of shielding the planet from hard ionizing solar radiation) indefinitely.
Which leads me to the question: what do the aliens have against sphere-shaped planets that they're willing to go to all this trouble?