Laver Cup is an exhibition tournament that is not regulated by the ATP or ITF, and therefore the organizers can decided what rules to play with.
In 2017, for the first version of this tournament, the match format according to the tournament webpage is the following:
Both singles and doubles will be best of three sets with ad scoring. In the event of split sets, the third set will be a 10-point match tiebreaker.
Why the organizers decided to use this specific format is up for discussion. There isn't a consensus about no-ad scoring in the circuit, as seen on this article, so maybe this was a way to show you can keep ad scoring while still making matches shorter and more predictable in length. This last part is something that does have more backing from players and organizers since it could help prevent injuries, while TV has been pushing for this for commercial/scheduling purposes. It also brings ad scoring to
Examples of trials for shorter match formats can be seen in the 2017 Hopman Cup (doubles played in Fast4 format) and the 2017 Next-Gen Finals will be first to 4 games with tie break at 3 all with no-ad games (ATP website).