I read a lot of literature already and never heard of a mantis species wiped out by another. The only species that are endangered are threatened by habitat loss or small distribution areas. Most of those also co-occur with other, larger, species. As I said before, mantids can well coexist in the same habitat. The more species there are, the lower the abundances of individual species. It must be said in this context, that the Nearktis (= N-America) is very empoverished regarding its mantid fauna, that is, it is not as saturated with species as latitude and the climatic conditions would suggest. While most N-American taxa are more diverse than the European counterparts (birds, mammals, reptiles, butterflies, beetles etc.), the situation is reversed in mantids. That's why the 4 new mantid species were able to colonize the N-American continent so fast. As some of the S-American taxa seem to have invaded S-America via N-America, the reasons for the depauperate state isn't to be found in missing chances but rather in extinction events during the Pleistocene and possibly the Pliocene. As a tropical group, mantids do not well with Ice Ages...Tenodera is a paleotropical group which spread out into the temperate zone of East Asia (not a temperate group as suggested by Hurd et al.). You see this in the fact that T. sinensis doesn't have an obligate diapause: if you keep the ooths warm, they will hatch. Temperate species adjust their diapause via daylight cycle, not temperature.
A speciation event only occurs if a reproductive barrier is established. The nature of this barrier may be diverse. Geographical barriers are the best known ones. T. sinensis, aridifolia and angustipennis are very similar and most probably closely related. If a geographical barrier facilitated speciation, they must have been separated for a long period of time, long enough for reproductive incompatibilities to become established. Subsequent overlap of area wasn't a problem then. It has to be considered that there are several other species known, which may or may not be closely related to one of the three.