Definitions
The definition of "successful" is a little unclear here.
Does it mean "restored to full health"? Clearly not, because the next line of the article states:
However, it is not uncommon to see a loss of strength.
Does it mean "removed all pain"? In that case, the answer is no. (See below.)
Perhaps it merely means "patient felt better than before" or even "patient ended up no worse"?
Surgery As Last Resort
Note that the original link, and the cites below, treat surgery as a last resort, when other less-invasive treatments have failed. As such, it isn't fair to compare its effectiveness to other treatments. Its value is in how well it treats those patients for whom the less dangerous methods have failed.
No good evidence in 1992
In 1992, some researchers tried to perform a meta-analysis to establish the evidence before or against surgery and other techniques for "lateral epicondylitis of the elbow" (which is more commonly known as Tennis elbow.)
- H Labelle; R Guibert; J Joncas; N Newman; M Fallaha; and CH Rivard, Lack of scientific evidence for the treatment of lateral epicondylitis of the elbow. An attempted meta-analysis, J Bone Joint Surg Br September 1992 vol. 74-B no. 5 646-651
They weren't impressed with the evidence they found:
we therefore concluded that there was insufficient scientific evidence to support any of the current methods of treatment.
Limited evidence in 2010.
In 2011 (based on earlier data), a systematic review was performed by a Cochrane team:
- Buchbinder R, Johnston RV, Barnsley L, Assendelft WJJ, Bell SN, Smidt N. Surgery for lateral elbow pain. Cochrane Database of Systematic Reviews 2011, Issue 3. Art. No.: CD003525. DOI: 10.1002/14651858.CD003525.pub2
They looked at a couple of found some evidence that some of the surgical techniques lead to people giving lower pain/disability scores afterwards than other surgical techniques.
However:
Due to a small number of studies, large heterogeneity in interventions across trials, small sample sizes and poor reporting of outcomes, there was insufficient evidence to support or refute the effectiveness of surgery for lateral elbow pain.
[...]
Implications for practice
There is a paucity of high quality evidence to either support or discourage the use of surgical interventions for lateral elbow pain. Patients undergoing surgical procedures for lateral elbow pain should do so in the knowledge that it is still an unproven treatment modality in this condition.
Conclusion
While the definitions are unclear, there doesn't seem to be evidence to support the claims made that 80-90% of surgeries being successful.
You can decide for yourself whether the Center for Sports Medicine is properly informing potential patients of the risks, as recommended by Cochrane.