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At 13th level, the Thief rogue gains the Use Magic Device feature, which states:
By 13th level, you have learned enough about the workings of magic that you can improvise the use of items even when they are not intended for you. You ignore all class, race, and level requirements on the use of magic items.
Would this ability overcome the class restrictions of a wizard, and thereby allow a Thief rogue to use a wizard's spellbook?
As mentioned by Krzysztof Skibiński, a spell book is not a magic item. The Thief Rogue's sub-class ability Use Magic Device allows your rogue to use a magic item that they normally would not be allowed to use.
For instance, a Rod of Resurrection (DMG, p. 197) normally only requires attunement by a Cleric, Druid, or Paladin to be used. This ability would allow your rogue to attune to and use it.
Wizard's Spellbook is not a magic item. It's their Spellcasting class feature that allows them to prepare spells from their (and only their) book, which they can later cast.
Spellcasting
As a student of arcane magic, you have a spellbook containing spells that show the first glimmerings of your true power. (...)
Preparing and Casting Spells
(...)
You prepare the list of wizard spells that are available for you to cast. To do so, choose a number of wizard spells from your spellbook (...)
(Emphasis mine)
