Answer: Hello mate!
The orbit of the planets is around the sun, which means that the principal contribution in the forces is due to the sun's gravity.
But, it is true that planets experience a gravitational force due other planets, and this also contributes to the actual orbits (suppose that you "remove" a planet, then the orbit of the other planets may change)
So this is false; the actual statement would be true if it was:
"Gravity holds planets in orbit because planets are attracted to each other’s and the sun gravitational force."
And there are other contributors, like satellites and such, but those are really minor compared with the previous contributions.