Based on what we've seen in the show, there's nothing that leads us to believe it requires physical force in the same sense that a normal weapon requires force to kill a human (by damaging their internals).
You can clearly see that the Walker's body shatters all over when Sam stabs him. The same thing happens when Jon Snow strikes a Walker. Though that was Valyrian steel and not dragonglass, the result is the exact same.
If physical force was the cause of death, it makes no sense why the Walker shatters completely and not just where they get struck with the weapon (you could argue that Jon hit him hard enough to "break the ice", but Sam clearly didn't). This strongly suggests that dragonglass/valyrian steel somehow breaks the magic seal that keeps Walkers alive, and thus their reaction to the weapon is unrelated to the force with which it is applied.
However, it is uncertain to what degree such a material can kill a Walker. It may possibly require penetrating the skin deep enough (again, the specifics are not known) rather than just touching their skin. I can't recall a situation in which Walker touched dragonglass/valyrian steel and whether they did or did not have a reaction to it.
Therefore, it's possible it requires some force, but that force is necessary to penetrate their skin rather than to cause the magic-dispelling reaction that kills them. Given that the Walkers wear armor compared to wights, that would suggest that their skin isn't particularly hard to penetrate (easier than the armor, at least).