Source: TW
Human genes involved in language
FOXP2
A Forkhead transcription factor that regulates genes involved in motor planning and neural plasticity. Mutations cause speech apraxia.
CNTNAP2
A neural cell adhesion molecule regulated by FOXP2. Variants associated with language delay, autism, and specific language impairment (SLI). Extant Homo sapiens have a subtle I345V variant, which might have a functional effect.
FOXP1
A Forkhead transcription factor related to FOXP2. Mutations lead to intellectual disability, speech incapability and severe language delay.
KIAA0319
A neural cell adhesion molecule with PKD and Ig domains involved in neuronal migration. Strongly linked to dyslexia and reading disorders.
DCDC2
Doublecortin domain protein involved in polymerization of microtubules in neurons during neural migration. Variants associated with dyslexia and phonological processing defects.
ROBO1 / ROBO2
A neural cell adhesion molecule with Ig and FN3 domains involved in guidance of axons during pathfinding in brain development. Linked to phonological deficits and language acquisition. Extant H.sapiens have gained derived regulatory changes which might affect linguistic capacity.
SRPX2
Secreted Sushi and HYR domain protein required for synapse formation in language-related brain areas. Mutations result in speech dyspraxia and Rolandic epilepsy.
ATP2C2
P-type ATPase involved in calcium transport and synaptic function. Variants associated with SLI and general language deficits.
CMIP
LRR domain protein with a possible signaling function. Variants associated with SLI and variation in language processing.
GRIN2A
Encodes a glutamate receptor subunit. Variants linked to epilepsy-related language regression (Landau–Kleffner syndrome).
Barring the cases noted above, TMK all the other genes listed above lack variants that might distinguish functionality is sapiens from Neanderthals or Denisovans. Hence, the basic genetic apparatus for language was pretty much there before divergence of these three Homo lineages: ~800 K years +++(5)+++
Defects
In some cases when the gene is defective, in other cases when there are variants affecting its expression rather than a defect in the coding sequence of the gene.
Couldn’t it just be that their effects of their malfunction happen to be felt more severely in language regions of the brain?
Regarding the 2nd question, I think the general answer is yes. Deleterious mutations in them do tend to result multiple neural defects some of which have a language effect.
The knock ins might not have language generating effects as there is more to the apparatus of language like the voice box and tongue. However, current evidence does suggest that some genes like FoxP1 and FoxP2 have a role in vocalizations of various vertebrates other than humans, e.g., bird calls and mouse calls etc