Let me start with the grammatical structure. But just briefly, the appearance of the word degree is indeed a mistake, and I will omit it in the discussion of grammar. I will say more about degree at the end.
The structure may be clearer if some (optional) commas are inserted:
Global temperatures have already risen 0.9℃, and continental temperatures 1.5℃, above pre-industrial levels.
This is in fact a combination of two constructions: gapping and right node raising (RNR).
Wikipedia has an article on this, here. CGEL says the following (p. 1337):
4.2 Gapped coordination (Kim is an engineer and Pat a barrister)
Gapped coordinates are structurally incomplete clauses: the predicator is omitted, so that there is a gap in the middle of the clause. Compare:
 i Kim is an engineer and Pat is a barrister. [basic coordination]
ii Kim is an engineer and Pat __ a barrister. [gapped coordination]
The gap, marked in [ii] by ' _', is interpreted anaphorically from the underlined antecedent in the first clause. Usually a gapped coordination is semantically equivalent to a basic coordination in which there is repetition rather than a gap [the repetition need not be exact, since agreement features are irrelevant: the basic counterpart of Kim is an engineer and the two boys doctors will have are, not is], as [ii] here is equivalent to [i]. Gapping is possible only when the coordinates have parallel structures: the gap is flanked by elements which match elements of like function flanking the antecedent. In [ii], for example, Pat matches the subject Kim and a barrister matches the predicative complement an engineer. In multiple coordination all the coordinates after the first can be gapped: Kim is an engineer, Pat_a barrister, and Alex _a doctor. [The term 'gapping' is taken from formal grammar; there is no established term in traditional grammar for this construction. It should be emphasised, however, that there are numerous constructions that we analyse in terms of a gap, and the term 'gapping* or 'gapped coordination* applies only to the one discussed in this section.]
Right node raising (RNR)
RNR is famous in linguistics circles for being challenging to account for. CGEL calls it delayed right constituent coordination (pp. 1343-1345). Wikipedia has a good article on it, here.
Here's CGEL (I'm borrowing from my answer to this question):
In this construction the constituent which in basic coordination would appear as the rightmost element of the first coordinate is held back until after the final coordinate:
 i She knew of m͟y͟ ͟o͟t͟h͟e͟r͟ ͟w͟o͟r͟k͟ but never mentioned it. [basic coordination]
ii She knew of but never mentioned m͟y͟ ͟o͟t͟h͟e͟r͟ ͟w͟o͟r͟k͟. [delayed right constituent]
In general, the effect is to heighten the contrast between the coordinates by removing from them material that would be the same in each. But the construction is appreciably more difficult to process than basic coordination, both for the addressee, who has to hold the first coordinate in mind until the sense is completed at the end, and for the speaker, who has to plan ahead to ensure that each coordinate ends in a way that syntactically allows completion by the delayed element—as knew of and never mentioned both allow completion by an NP complement.[Examples are found where this condition is not satisfied. One case is illustrated in ?I always have and always will v͟a͟l͟u͟e͟ ͟h͟e͟r͟ ͟a͟d͟v͟i͟c͟e͟, where the plain form value is an admissible continuation of will but not of have: compare basic I have always v͟a͟l͟u͟e͟d͟ her advice and always will v͟a͟l͟u͟e͟ it. Another involves coordination of comparisons of equality and inequality: ?It's as good or better t͟h͟a͟n͟ ͟t͟h͟e͟ ͟o͟f͟f͟i͟c͟i͟a͟l͟ ͟v͟e͟r͟s͟i͟o͟n͟, where as good takes a complement headed by as not than. Such examples are not fully grammatical and would generally be avoided in monitored speech and writing; the second can be corrected to It's as good as or better than t͟h͟e͟ ͟o͟f͟f͟i͟c͟i͟a͟l͟ ͟v͟e͟r͟s͟i͟o͟n͟.] Characteristically, there is a prosodic break after the final coordinate, signalling that the element that follows relates to the whole coordination, not just to the final coordinate.
As you can probably see now, your sentence has both gapping and RNR. If we omit above pre-industrial levels, it would have just gapping, i.e. we could say that
Global temperatures have already risen 0.9℃ and continental temperatures __ 1.5℃.
is simply a gapped coordination, whose basic counterpart is
Global temperatures have already risen 0.9℃ and continental temperatures have already risen 1.5℃.
On the other hand, if we eliminate the gap but keep above pre-industrial levels, we have a clean RNR (I will insert optional commas for clarity):
Global temperatures have already risen 0.9℃, and continental temperatures have already risen 1.5℃, above pre-industrial levels.
Here above pre-industrial levels is the 'delayed right constituent' from CGEL's analysis. The corresponding basic coordination reads
Global temperatures have already risen 0.9℃ above pre-industrial levels and continental temperatures have already risen 1.5℃ above pre-industrial levels.
The word degree
As Janus mentioned, the appearance of the word degree is simply a mistake. It should be either
temperatures have risen 1.5℃ above pre-industrial levels
temperatures have risen 1.5 degrees Celsius above pre-industrial levels.
There are a few caveats.
One concerns whether there should be a space between the number and the degree symbol. According to the Chicago Manual of Style (CMOS, 10.58),
In SI usage as in general usage, a space usually appears between the numeral and any abbreviation or symbol. Contrary to general usage, however, SI usage also stipulates a space before a percentage sign (%) or before a degree symbol used for temperature (compare the advice in the introduction to the table at 10.49). In expressions of degrees, minutes, and seconds, SI usage shows (but does not stipulate) a space between quantities. Many publications do not observe these exceptions, and Chicago does not require them in its publications.
SI style Chicago style
22 °C 22°C
22° 14′ 33″ 22°14′33″
0.5 % 0.5%
Another caveat is Associated Press Stylebook, which dispenses with the degree symbol:
When giving a Celsius temperature, use these forms: 40 degrees Celsius or 40 C (note the space and no period after the capital C) if degrees and Celsius are clear from the context.
Many academic publications agree with the recommendations of CMOS:
- This book presents the energy system roadmaps necessary to limit global temperature increase to below 2°C, in order to avoid the catastrophic impacts of climate change. (source)
- All-cause mortality increased by up to 51% above the average in those over 75 years of age for each degree Celsius above 41°C. (source)
However, National Institute of Standards and Technology (NIST) follows the SI recommendations (source):
On the widely used Celsius temperature scale, water freezes at 0 °C and boils at about 100 °C. One Celsius degree is an interval of 1 K, and zero degrees Celsius is 273.15 K.
So does the U.S. Government Printing Office—Style Manual.
The Oxford Guide to Style says:
Express a degree of temperature in figures, such as 40 °C (no point).
There is a space of the line (or thin space in scientific and technical
work) between the figure and degree sign. Since the ° forms part of the
temperature unit rather than the figure, it is clarified by and joined to a
unit: there is no space between it and the abbreviated unit: 40 ° C is