No. There is no Death Penalty for a Non-Jew learning Torah.
The Quote
“A goy (Gentile) who pries into The Law (Talmud) is guilty of death.”
Sanhedrin 59a
The Reality
The quote is accurate in that the words that it says are actually there. But it lacks the background to understand that this is not an actual death penalty and that it’s simply one rabbi’s opinion.
First off, let’s take a look at the actual quote:
The first thing to keep in mind is that very often, the Talmud will exaggerate something to emphasize a point. That is what is happening here. In order to emphasize the point that the Torah was given to the Jews and not the non-Jews, Rabbi Yochanan goes so far as to state that a non-Jew who learns Torah is deserving of death.
A similar phenomenon occurs elsewhere. In Shabbos 114, where one rabbi states that a Torah scholar who wears stained clothing is liable to the death penalty.
The reality, however, is that there is no death penalty for this. Elsewhere in Sanhedrin (Mishna, chapters 6-10) all the capital crimes are listed out. A Torah scholar with a stain on his clothing is not there, and neither is a non-Jew who learns Torah.
Rabbi Hiyya was simply exaggerating to stress how important it is for a Torah scholar to have a neat and respectful appearance.
The same applies to a non-Jew learning Torah. There is no actual death penalty involved for this. There is absolutely no record anywhere of any Jewish court executing a non-Jew for learning Torah.
One Rabbi's Opinion
Whenever you see fake Talmud “quotes,” the person who is distributing them is often operating under the assumption that the Talmud is a second “Jewish Bible” and that everything there is Jewish dogma.
The reality is that the Talmud is largely a collection of legal arguments. Rabbis discuss various legal and theological points and present their opinions. As a result, not everything that you see in the Talmud is accepted Jewish law or normative Jewish thought. Indeed, the majority of opinions recorded in the Talmud are, in fact, rejected.
This quote is one rabbi’s opinion. What you almost never see is the quote that immediately follows it:
So, here you have another opinion that says just the opposite — not only is it not bad for a non-Jew to learn Torah, but in fact it is meritorious and he is compared to a High Priest.
Summary:
The quote here is accurate, but is not meant to be taken literally and there are no recorded cases of any non-Jew ever being put to death for studying Torah. It is simply an exaggeration (by one rabbi) to emphasize the point that the Torah is the inheritance of the Jewish people.