DeeAnn - I disagree. They are clearly alternative, unconnected definitions, not just in the source you suggested as quoted above, but also in others. Wikipedia, for example, begins a transgender discussion with several clearly different alternative definitions:
"Transgender people experience a mismatch between their gender identity or gender expression and their assigned sex. Transgender is also an umbrella term because, in addition to including trans men and trans women whose binary gender identity is the opposite of their assigned sex (and who are sometimes specifically termed transsexual if they desire medical assistance to transition), it may include genderqueer people (whose identities are not exclusively masculine or feminine, but may, for example, be bigender, pangender, genderfluid, or agender). Other definitions include third-gender people as transgender or conceptualize transgender people as a third gender, and infrequently the term is defined very broadly to include cross-dressers."
There is little similarity between the definitions, as you suggest, and more appropriately, they are rather independent and serve different purposes.
Your own definition begins with the supposition that "if you dress in the clothes and trappings of the gender that is opposite to your assigned at birth gender, you are Transgender" (another definition for transgender). You simply dictate all crossdressers are transgender. Maybe too simple and maybe offensive or unacceptable to crossdressers. You also disqualify any consideration of frequency, degree, extent of dressing, intent or purpose of crossdressing. That also seems too simple.
I respect your view but I think it does represent the consistent label of "transgender" pushed on crossdressers.