This law is applying its +25 happiness bonus only to the local system. If you read the flavor text on the law's tooltip, it's pretty obvious this is supposed to be applying empire-wide.

The issue is a bad <Path> entry specified in Endless Space 2\Public\Simulation\TemporaryEffectDefinitions.xml. You can fix this yourself by opening that file, and at the very top, you will see this:

 <!-- Gameplay -->     

<TemporaryEffectDefinition Name="ColonyHappinessBoost" Category="LawEffects" Duration="5">         

        <Path>ClassColonizedStarSystem</Path>         

        <SimulationDescriptorReference Name="TemporaryEffectColonyHappinessBoost"/>     

</TemporaryEffectDefinition>

Replace the above section with this (only one line is changed, line #6 of the file):

 <!-- Gameplay -->     

<TemporaryEffectDefinition Name="ColonyHappinessBoost" Category="LawEffects" Duration="5">         

        <Path>../ClassEmpire,EmpireTypeMajor/ClassColonizedStarSystem</Path>     

        <SimulationDescriptorReference Name="TemporaryEffectColonyHappinessBoost"/>     

</TemporaryEffectDefinition>

This will cause the New Colony law to work as intended and apply an Empire-wide happiness bonus of +25 for 5 turns. I have tested it thoroughly, and the Republic government version works now correctly as well (it provides +35 for 5 turns). 

I wondered why this law was so... underwhelming.

Moved to the Bug Reports forum. Thanks for the heads-up and the fix! I've passed it on to the team.

Good work Kornstalx!