Regarding the general rules about women wearing men's clothing, from Halachos for Monday, May 6, 2013 in this article:
1) A woman may not wear men's clothing, including men's pants and
men's hats, as doing so is a biblical prohibition of "Lo Yihyeh Kli
Gever Al Isha, a man's clothing shall not be on a woman" (Devarim
This prohibition extends to any action done by a woman to make her
look like a man, including shaving in a masculine manner.(See Rashi
ibid. and Shulchan Aruch Yoreh Deah Siman 182:5)
2) Some Poskim rule that the prohibition is only in place when done
for the express purpose of looking like a man, but if wearing a man's
garment for protection from the sun, rain or other elements it would
be permitted.(Taz on Shulchan Aruch Yoreh Deah Siman182 S"K 4)
However, other Poskim are stringent, and it is best for a woman to
avoid men's clothing at all costs. (Ruling of the Bach quoted in Taz
Item 2, above, states a leniency, in general.
Regarding the specifics of the shirt that you mention, I have to locate another article that I saw that deals with the specifics of shirts and pants. (It may have been written by someone from OU.) It states a general rule that clothes that have become the norm to be worn by both genders such as jeans, slacks and shirts do not pose a violation of this halacha. Of course, it assumes that the clothing being worn meet tzniut standards.
I will try to edit this answer once I can locate that source.
Somewhat aside - women who exercise wear gym shorts and sweats. I am assuming that since this is the norm for exercising, there is no violation, but, perhaps, the leniency is restricted only to exercising and not, e.g., grocery shopping?