I don't think there's a norm or many results for stuff screwed into a living tree (think bark thickness, diameter, grain irregularities etc), but if you naively take this equation, then p_crit = 108.25 * 7552 (kg/cum)2 * 8 mm * 80 mm = ~40000 kg. It sounds high, but that's static (!), and completely disregarding wetness, the other screws in close proximity, or anything else that might affect the quality of the connection long-term (like the recurring load of your workout, rust, mold etc.). Also, even if the screws end up holding the equivalent of a car's weight, what about the connection plate you used? And how long will everything keep supporting this crazy load? It's just a ridiculous design. Fix it if you want to use it for more than a few months.
You're getting a significant increase in force because of the crazy lever. Just imagine holding the part attached to the tree in your hands and keeping it from turning. I estimated tenfold without measurements, but you can calculate everything easily by sketching it like this and solving the force and moment equilibrium.
If you want to be cool, do the math, then do it again with another support on top. You'll see the horizontal force shrink to about half of your load, all with the power of math. Wow. Very numbers.
If you actually run the numbers and have any problems, post. Cheers.
Disclaimer: I haven't worked with wood and don't know the precautions when stressing it to its limits, and I didn't check the source on that website. Also the sketch is missing vertical reaction forces, sue me.