Yes. Very much it does. It's been 35 years since I played Laser Chess, so perhaps there are some minor differences in the rules. But it describes a game so close to Laser Chess that it immediately brought the game to mind.
You can move a piece 1 or 2 spaces in a single direction (1 east, or 2 east, but not 1 north east unless that was used as two moves). You could also rotate on your turn. Firing a laser was optional.
In Khet, you can move one piece 1 adjacent spot (any of the 8) or rotate (not both) and you always fired the laser.
The rules are different - and the rules are patented.
If you had different rules that weren't covered by the claims, it would be a different game.
Laser strategy game board - https://patents.google.com/patent/US20080054563A1/en - that's a different game that was patented after Khet.
https://youtu.be/4nQaWJEBFNk (and if you want to play a digital version https://store.steampowered.com/app/312720/Khet_20/ ) vs https://archive.org/details/laserch or https://archive.org/details/msdos_Laser_Chess_1994
They are different games with different rules.
Strategic board game https://patents.google.com/patent/US6981700B2/en
https://en.wikipedia.org/wiki/Arimaa
While that plays with animal pieces, there's a 1:1 mapping from traditional chess pieces to Arimaa pieces and it's played on the same board.
Give https://patents.google.com/patent/US7264242B2/en a read and see if that describes the computer game. If not, it's something different.
Going into the patent citations there are a number of other laser board games that it references that are different games with different claims as to what they patent. Here's a different board game with lasers that predates Khet - https://patents.google.com/patent/US5145182A/enIs it different? Do they claim different things? Having something similar isn't necessarily legally similar.
Blue and Gray is a checkers game that is played on a checkers board with checkers pieces and is distinct enough to receive a patent.
Trademarks protect names. Copyrights protect that text or music or ... Patents protect that idea - the rules and mechanics of that game.
And more specifically the claim about movement: Does that describe Laser Chess?