Question:If you are married and your spouse is texting other people outside the marriage of the opposite sex, is that a form of cheating or adultey?
No. Adultery is having sex with someone when either is married to someone else. People talk with other people all the time and texting is a modern form of talking. The fact that talking is occuring says nothing about whether a person is faithful or not to a marriage.
What your question does indicate is that you are being overly possessive in regards to your wife. "Love is patient, love is kind and is not jealous; love does not brag and is not arrogant, does not act unbecomingly; it does not seek its own, is not provoked, does not take into account a wrong suffered, does not rejoice in unrighteousness, but rejoices with the truth; bears all things, believes all things, hopes all things, endures all things" (I Corinthians 13:4-7 NASB).