The Anti-Terrorism Act of 1987 does not give a list of terror groups. It refers only to the PLO. It says:
...Congress determines that the PLO and its affiliates are a terrorist organization and a threat to the interests of the United States, its allies, and to international law and should not benefit from operating in the United States....It shall be unlawful, if the purpose be to further the interests of the Palestine Liberation Organization or any of its constituent groups, any successor to any of those, or any agents thereof, on or after the effective date of this chapter...(3) notwithstanding any provision of law to the contrary, to establish or maintain an office, headquarters, premises, or other facilities or establishments within the jurisdiction of the United States at the behest or direction of, or with funds provided by the Palestine Liberation Organization or any of its constituent groups, any successor to any of those, or any agents thereof.
The prohibition of having an office in the US can be waived annually, first by the President and since 2010 by the Secretary of State. But the law is still in force, and that is what Abbas wants to abolish.
One of the proofs given by the law of the PLO's terrorist nature was a reference to its 1968 charter, which ways (among other things) that "armed struggle is the only way to liberate Palestine, thus it is an overall strategy, not merely a tactical phase."
The 1968 PLO Charter supporting terror is still in force, today. It is shown in PLO websites today without any caveat or indication that it has been superseded.
Don't take my word for it. An analysis by Heba Baydoun in Ma'an last year looked at this exact question and concluded that the supposed vote to change the charter held in front of Bill Clinton in 1998 was all a show and had no legal force.
She says that the meeting that was held on December 14, 1998 in Gaza with Clinton in attendance where there was a supposed "vote" to amend the charter was not an official meeting of the Palestinian National Council. If you look at the list of official meetings of that council, it isn't listed - it happened between the 21st (1996) and 22nd (2009) meetings. The official invitation to the meeting didn't indicate that it was anything other than a gathering to listen to Clinton speak. Unlike official meetings, there was no opening session, no count of a quorum - many of the attendees who "voted" were not members of the National Council. There was no agenda, the president and vice presidents of the National Council did not attend (which is mandatory,) the secretary didn't lead the session, there was no final statement at the end of the meeting, and it was never recorded among the records of official National Council meetings.
It was political theatre to fool the US into thinking that the charter was changed. The show of hands vote was purely symbolic.
Moreover, if the charter had been amended and the offending terrorist sections removed, where is the new charter? It has never been published.
Because it doesn't exist.
(On April 24, 1996, during the official 21st PLO National Council meeting, one decision was that its Legal Committee would reformulate the National Charter, and it will be presented to the Central Council. That never happened.)
So the current PLO charter says:
Armed struggle is the only way to liberate Palestine. This it is the overall strategy, not merely a tactical phase. The Palestinian Arab people assert their absolute determination and firm resolution to continue their armed struggle and to work for an armed popular revolution for the liberation of their country and their return to it .Commando action constitutes the nucleus of the Palestinian popular liberation war.The partition of Palestine in 1947 and the establishment of the state of Israel are entirely illegal, regardless of the passage of time, because they were contrary to the will of the Palestinian people and to their natural right in their homeland.The Balfour Declaration, the Mandate for Palestine, and everything that has been based upon them, are deemed null and void. Claims of historical or religious ties of Jews with Palestine are incompatible with the facts of history and the true conception of what constitutes statehood. Judaism, being a religion, is not an independent nationality. Nor do Jews constitute a single nation with an identity of its own; they are citizens of the states to which they belong.The Arab Palestinian people, expressing themselves by the armed Palestinian revolution, reject all solutions which are substitutes for the total liberation of Palestine and reject all proposals aiming at the liquidation of the Palestinian problem, or its internationalization.Zionism is a political movement organically associated with international imperialism and antagonistic to all action for liberation and to progressive movements in the world. It is racist and fanatic in its nature, aggressive, expansionist, and colonial in its aims, and fascist in its methods. Israel is the instrument of the Zionist movement, and geographical base for world imperialism placed strategically in the midst of the Arab homeland to combat the hopes of the Arab nation for liberation, unity, and progress. Israel is a constant source of threat vis-à-vis peace in the Middle East and the whole world. Since the liberation of Palestine will destroy the Zionist and imperialist presence and will contribute to the establishment of peace in the Middle East, the Palestinian people look for the support of all the progressive and peaceful forces and urge them all, irrespective of their affiliations and beliefs, to offer the Palestinian people all aid and support in their just struggle for the liberation of their homeland.The demand of security and peace, as well as the demand of right and justice, require all states to consider Zionism an illegitimate movement, to outlaw its existence, and to ban its operations, in order that friendly relations among peoples may be preserved, and the loyalty of citizens to their respective homelands safeguarded.
Anyone who says that the PLO has abandoned these principles needs to show proof. There is none.
Therefore, the PLO is still a terror organization, even if it has temporarily chosen for tactical reasons not to emphasize that aspect of its "resistance." And we know that because the Fatah political platform of 2009, way after Oslo, still emphasizes that "armed struggle" as legal and rightful - and that platform is also in force today.