This a DM Ruling Case
The rule doesn't specify that an Ability Check or Contest has Disadvantage when a creature is Restrained. (Appendix A; Conditions)
• A restrained creature’s speed becomes 0, and it can’t benefit from
any bonus to its speed.
• Attack rolls against the creature have advantage, and the creature’s attack rolls have disadvantage.
• The creature has disadvantage on Dexterity saving throws.
Granting Advantage/Disadvantage in such a case is a DM option, and that is pointed out in the rules. This is a case where rulings by the DM are called out as integral to the game (Advantage; Basic Rules p. 57; PHB p. 173).
You usually gain advantage or disadvantage through the use of special abilities, actions, or spells. Inspiration can also give a character advantage (as explained in chapter 4, “Personality and Background”). The DM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result.
If it makes sense to the DM that this circumstance, being stuck in the web, grants Disadvantage to an Acrobatics check then the DM will rule that Disadvantage applies to that circumstance. The DMG supports this approach. (DMG p. 239).
Advantage and disadvantage are among the most useful tools in your DM's toolbox. They reflect temporary circumstances that might affect the chances of a character succeeding or failing at a task.
RAW would also seem to indicate that shoving a bound pc is just as difficult as shoving a free pc.
The web that restrains him is easily seen as having enough of a grip on the character that it prevents him from falling down or moving suddenly, as with a shove.