What is the effect of adding eggs to a pastry dough?
While many bread and pastry products do depend critically on the formation and management of gluten from wheat flours, this is not universally true.

Some types of pastry have structure dependent more on the starch networks which is the other major component of wheat flours; the texture and properties of these pastries is often dependent on the gross mechanical manipulation of the structures, depending on how the product is manipulated.

American style pie crust is a case in point.  Flaky pie crust is generally manipulated in a manner which minimizes gluten production:  low hydration, resting periods, and minimal mechanical manipulation.

The structure and flakiness emerges because the dough is essentially a series of butter flakes or bits, coated in starch.  When baked, the starches gelate and steam from the dough pushes the butter pockets apart before the butter is fully melted and integrates into the dough structure.  This is not dependent on gluten formation.

Taking La Cucina Italiana's pasta frola recipe as typical, it appears that pasta frola has more in common with flaky pie crust than it does with bread or puff pastry, where gluten formation is key.

The egg in the dough will contribute mostly water (eggs are 75% water).  The remainder is primarily proteins (from the albumen in the egg white, and fats from the yolk).

This will somewhat tenderize the final pastry, and contribute an eggy flavor.  It certainly does interfere with gluten formation, helping prevent a tough outcome, except in this application, gluten formation simply is not key.  It will also contribute to the final color, both from the yellow pigments in the yolk, and by slightly promoting browning.