Is it legal for a step-dad that does not claim his step child to press charges on a 19 year old male who is casually seeing the step-daughter who is 16 if the birthday of the male is 8/16/87 and the step-daughter's birthday is 1/22/91? Can anyone at all press charges on the male if the daughter does not want to, being that sex of any kind was never initiated? The male now lives over 300 miles away, and the two still want to be a 'couple.'

Yes, it is legal for the step-dad to file a complaint with police.
If any state laws have been violated, it would be up to the prosecuting attorney to determine if charges will be filed.

If it's determined through an investigation that there was no sexual contact, no charges would be filed. If it's determined that sexual contact did take place with a minor under the age of 17 and there is more than 3 years (36 months) between the two of you in age, you could be found in violation of 21.11.

§ 21.11. INDECENCY WITH A CHILD.
(a) A person commits an offense if, with a child younger than 17 years and not the person's
spouse, whether the child is of the same or opposite sex, the person:
(1) engages in sexual contact with the child or causes
the child to engage in sexual contact; or
(2) with intent to arouse or gratify the sexual desire
of any person:
(A) exposes the person's anus or any part of the
person's genitals, knowing the child is present; or
(B) causes the child to expose the child's anus
or any part of the child's genitals.
(b) It is an affirmative defense to prosecution under this
section that the actor:
(1) was not more than three years older than the victim
and of the opposite sex;
(2) did not use duress, force, or a threat against the
victim at the time of the offense; and
(3) at the time of the offense:
(A) was not required under Chapter 62, Code of
Criminal Procedure, to register for life as a sex offender; or
(B) was not a person who under Chapter 62 had a
reportable conviction or adjudication for an offense under this
section.
(c) In this section, "sexual contact" means the following
acts, if committed with the intent to arouse or gratify the sexual
desire of any person:
(1) any touching by a person, including touching
through clothing, of the anus, breast, or any part of the genitals
of a child; or
(2) any touching of any part of the body of a child,
including touching through clothing, with the anus, breast, or any
part of the genitals of a person.
(d) An offense under Subsection (a)(1) is a felony of the
second degree and an offense under Subsection (a)(2) is a felony of
the third degree.