Is an Uber driver considered an SSTB?

No.

According to the Proposed Regulations, the "reputation or skill" thing is extremely limited.  Here is what it says:

In sum, the Treasury Department and the IRS believe that the “reputation or skill” clause as used in section 199A was intended to describe a narrow set of trades or businesses, not otherwise covered by the enumerated specified services, in which income is received based directly on the skill and/or reputation of employees or owners.  Additionally, the Treasury Department and the IRS believe that “reputation or skill” must be interpreted in a manner that is both objective and administrable.

Thus, proposed §1.199A-5(b)(2)(xiv) limits the meaning of the “reputation or skill” clause to fact patterns in which the individual or RPE is engaged in the trade or business of
(1) receiving income for endorsing products or services, including an individual’s distributive share of income or distributions from an RPE for which the individual provides endorsement services;
(2) licensing or receiving income for the use of an individual’s image, likeness, name, signature, voice, trademark, or any other symbols associated with the individual’s identity, including an individual’s distributive share of income or distributions from an RPE to which an individual contributes the rights to use the individual’s image;o
(3) receiving appearance fees or income (including fees or income to reality performers performing as themselves on television, social media, or other forums, radio, television, and other media hosts, and video game players).
https://www.irs.gov/pub/irs-drop/reg-107892-18.pdf#page=65