IMO, it comes down to the details. Types of training being done, frequency of the training, relative intensity, and order of the training in a week. It all needs to come together "like a symphony".
The thing to remember is that, no one single workout or type of workout is sufficient. The key is consistent training with sufficient intensity for the type of training you are doing and ensuring that you will also retain enough energy for your next workout.
With that said, in my training, I'm only able to do 1 or at most 2 pure interval training sessions a week. Most often I do one session and incorporate another one (or maybe even two) into my other training runs. For example, I might incorporate 6X150 into a 5 mile run.
You'll have to determine if tennis is like interval training for you. I play a decent game of singles, but I don't really see tennis as interval training for me. So for me, playing more than 2 matches a week is fine. I see no problem with playing multiple times per week and don't feel like the recovery from a match is comparable to a true interval session.
I could go into much more detail, but I doubt the interest level is really there along these lines for too many people. The general guideline I use for overall fitness for myself (and this I believe also makes me "tennis fit') is the ability to run a 5-K in 20-minutes (6:30 pace). To do this, you need to train in a variety of ways, intensities, distances. It's not really a difficult standard, but I find that being able to do this makes me fit enough for pretty much anything (and almost always fitter than my opponent).
At any rate, train smart, get fit, and stay healthy. Good luck.
Here's an article you might find interesting. I'd guess that playing tennis is mainly "aerobic interval training" as opposed to "anaerobic interval training", though doing anaerobic interval training once (maybe twice) a week will improve your tennis speed and fitness.
Aerobic intervals involve working between a low aerobic zone (55 percent to 65 percent of maximum) and a high zone (75 percent to 80 percent of maximum). Anaerobic intervals call for a work period falling within 80 percent to 95 percent of maximum heart rate, while the rest periods may drop to an aerobic zone or even lower (below 50 percent of maximum).
Although interval training is a valuable training tool, it should be used in moderation. Intervals, especially high-intensity ones that dip into your anaerobic zone, provide the most benefit when performed only one or two times per week, or you risk overtraining. Steady-state cardio training, at a zone of about 60 percent to 80 percent of maximum, still offers benefits for overall health and weight management.