Concept of "load sharing" is subject to shades of meaning and interpretation. However, in general, I submit that it means that load resisted by a member is somehow reduced.
However, for practical purposes......and as demonstrated (though with caveats noted below) by the simple though fine load-test illustrated above....the "board on top of beam" can be used to reduce deflection of, and bending moment in, the beam......... even though total load resisted by the beam is not reduced at all......and deformation of the two independent members is significantly different.
Based on standard calculations.........point load (P) at midspan of simple span causes midspan deflection that is 16-percent greater than midspan deflection caused by two equal loads (each P/2) placed at third-points of the beam.
As for the greater increase of deflection (compared to theory) that appears to have occurred in the above load test..........several factors are likely relevant ......including additional weight of white board (though that may be minor) and behavior of this specific wood beam. If same test is performed using several, more substantial (deeper) beams, deflections should average out to values resulting from standard calculations.
When length of "white board" member is equal to span of the lower beam........the 2 beams will share load similar to the condition for an upper beam oriented perpendicular to, and placed on top of, a lower beam. However, in such case, ends of the upper beam are supported by entirely different supports.
John F Mann, PE