Cure wounds is affected by Alchemical Mastery
In general, bonuses stack as long as they are from sources with different names (notable exception for proficiency bonuses):
Different game features can affect a target at the same time. But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap. (..) Game features include spells, class features, feats, racial traits, monster abilities, and magic items.
In this case, Cure Wounds is a spell that heals for 1d8 + your spellcasting modifier, to which you are also applying a class feature, "Alchemical Mastery", to further increase the healing. These are two different features so the fact both are telling you to add your Intelligence modifier does not matter.
So you can indeed combine these for 1d8+twice your intelligence modifier healing.
On the use of a focus for the spell1
Alchemical Mastery only affects spells when you are using a spellcasting focus:
When you cast a spell using your alchemist’s supplies as the spellcasting focus, you gain a bonus to one roll of the spell.
Fortunately, even though cure wounds has only Verbal and Somatic components (which would normally mean that you can't use a focus to cast it), an Alchemist uses their tools as a focus for every spell they cast. From the Tools Required section:
You produce your artificer spell effects through your tools. You must have a spellcasting focus—specifically thieves’tools or some kind of artisan’s tool—in hand when you cast any spell with this Spellcasting feature.
So it seems that this forces every Alchemist spell to use a spellcasting focus, allowing Alchemical Mastery to affect cure wounds.
Unearthed Arcana is playtest material
As usual, note that the Artificer content is still just playtest material and as such it is subject to change. The use of tools as a focus for every spell and associated rules and consequences may not have been properly thought out.
1. This section was completely inverted in a revision after a comment by Darth Pseudonym, noting that all artificer spells use a focus