Do not that this video seriously as to what it will likely look like. Keep in mind that as our sun grows into a red giant it would already be releasing extremely lethal solar flares. The inner planets being consumed by the sun would only come long, long after cooking them. Gravity would also be interesting at this point because the sun would have less mass. This video seems to take a lot of liberties as to how the physics of transitioning into a red giant would play out.

As others said, take that animation with a pinch of salt... but at the same time:

the center of mass of the sun doesn't change

The "center of mass" is a crutch that works fine at long enough distances, or when the gravitational force towards each part of an object can't tear chunks of another object apart. Like, you can 1G a human all you want, the limbs won't come flying apart until some serious pull in opposing directions gets applied (don't ask me for an exact value, but I've heard it's doable, for example with 4 horses).

As some of the Sun's mass (aka: a lot of mass) comes closer to Venus, there will be two things happening:

• The tangential components in opposing directions will become larger
• The "towards the center of mass" force, will grow with the square of the distance reduction to the closest bunch of mass(es)

Whether the approaching mass will be enough to overcome the gravitational force that keeps Venus in a single clump... or whether instead it will "rain Sun" down onto the surface of Venus... or neither... hard to say without some math (integral of the gravitational pull of the Sun's mass distribution in the inflated red giant phase at a given distance, compared to the gravity of Venus, the cohesive forces of the materials of Venus, and the pull [this time towards center of mass] of the Sun's mass that would come close to Venus), and a lot of guesswork as to how much mass would come how close to the planet.

Bonus: we can measure the "pulling apart" effect by going down into deep enough mines, where Earth's gravity slowly decreases even as you come closer to the "center of mass", because the spherical cap of mass above you, pulls you in the opposite direction.