The claim being made is that wind turbines kill more birds than oil spills. To find out whether this is true or not, we first need to find data on how many birds are killed annually by wind turbines.
The article cited referenced the American Bird Conservancy (ABC) as its source as to how many birds are killed by wind turbines within the US, which itself cited 3 different sources with 3 different estimates as to the amount of bird fatalities there are annually. Loss et al. estimates that it is 234,000 on average. Smallwood claims that the true number is closer to 573,093. Erickson et al. argues that it would be more accurate to claim it is around 291,000. One of these averages is much higher than the others, thus skewing the result and giving the ABC an average estimate of 366,000 birds from these averages. Not to mention, these studies are from 2013-2014, which the article itself even claims may be outdated due to the fact that we have tens of thousands more turbines compared to when these articles were first published. Considering how the rest of this article depends on extrapolating data from these studies to make its claim, I feel that this article is questionable in its modern-day applicability. Not to mention, there has been further research on how to make wind turbines safer, such as May et al.'s study on painting wind turbines reducing 70% of bird deaths and Gémard et al.'s research article on bird-detecting AI systems to let us further doubt the article's ability to further extrapolate its findings. Unfortunately, every other article I have found with estimates for wind turbine-related deaths reference either ABC's article or the studies mentioned within the article, so the total amount of bird deaths coming from wind turbines is inconclusive. However, for the sake of argument, let's assume that the article's extrapolation is reasonably accurate, and thus the annual bird death rate today is close to 1.17 million.
The comparison to oil spills is even harder to conduct when you consider the fact that oil spills do not happen on an annual basis. The National Oceanic and Atmospheric Administration has listed all significantly large oil spills on US waters from 1969 onwards (I chose specifically to compare with US waters due to the fact that the prior article uses exclusively American data as well). Again, in order to conduct a fair comparison, let's only utilize data related to oil spills from the 2000's onwards in order to get a similar time range.
Deepwater Horizon, 2010: From Haney et al., 800k.
Hurricane Katrina Oil Spills, 2005: No data found.
DBL 152, 2005: No data found
Citgo Refinery Oil Spill, 2006: From U.S. Department of the Interior, 11,896.
Kalamazoo River, 2010: From U.S. Fish & Wildlife Service, 22.
Taylor Energy Platform, 2004: No data found.
Mississippi Canyon, 2009: No data found.
Westchester, 2001: From National Oceanic and Atmospheric Administration, 582.
Bayport Channel Collision, 2019: No data found.
Eagle Otome, 2010: No conclusive data found, but according to ABC News, at least 4.
DM932, 2008: No data found.
Yet again, there is a problem found in missing data. As we can see, there have been 11 significant oil spills within the past 25 years, 5 of which have data on the amount of bird fatalities. The average of those 5 years is 162,500.8, with the Deepwater Horizon oil spill causing a massive skew. Regardless, for the sake of argument, let's assume that we can apply that average towards the other oil spills lacking data. Since we can assume that the rest of the years would have negligible bird deaths, there would be an average of 71,500.352 annual bird deaths caused by oil spills within the US.
1.17 million to 71,500 is an inarguable and obvious comparison. If these numbers are to be trusted, then yes, windmills do kill birds more than oil spills do and by a significant margin. However, I believe that we lack the conclusive data required to make such an argument.