The question actually involves whether the laser is considered a "blade" that cuts the hair or a "fire" that burns the hair off. However, the gemoro in nazir talks about the hashchasa (destruction) of the beard as being forbidden which would mean that the use of the laser is similar to the cutting of the hair by a razor. Note that even a razor is not "permanent" as it grows back. I deal with the similar question of using a laser to cut during shechita at If you shecht with a light saber, is the animal kosher?. In spite of the title, the concept can be dealt with seriously.
Note that the Rambam states in H. Avodas Zarah 12:8:
ואינו חייב עד שיגלחנו בתער--שנאמר "ולא תשחית, את פאת זקנך" (ויקרא יט,כז), גילוח שיש בו השחתה; לפיכך אם גילח זקנו במספריים, פטור. ואין המתגלח לוקה, עד שיסייע.
One is liable only when one shaves with a razor, as [implied by Leviticus 19:27]: "Do not destroy the corners of your beard." [We can infer that this applies only] to shaving which utterly destroys [one's facial hair]. Therefore, a person who removes his beard with scissors is exempt.
This can imply that "shaving" with a device such as this, which uses light as a "blade" may be similar enough to a razor, to be asur in the same way. The Gemoro in Nazir 40 - 41 discusses the reason that a razor is required and why other kinds of "shaving" are not asur. I have not yet seen a discussion of "burning" off the hair of a beard yet and cannot reach a conclusion on that matter.
I do not actually know if the halacha has been dealt with yet, but it may also involve the concept of ma'aris ayin (appearance of doing something wrong).
My own personal opinion would be that it should at least be avoided since it does appear to be hashchasa (destruction) of the hair and is more like a razor than a chemical depilation. However, this is not definite.