I think that complies with the rules as each leg can move up and down then separately can move forwards and backwards- it is by combining these 2 motions that the walking is achieved.
I imagine that you could replace the servos with a continuous motor running through a cam mecahnism to get a reciprocating motion like the one which is given by the servo.
I also imagine you could add more legs to the mechanism and if you had a separate motor for the forwards/backwards motion for each side then you could get better steering.
It would never be the fastest thing in the world but it would be quite basic to make.