That picture is of the Real Irish Republican Army (Real IRA), a splinter group from the Provisional IRA which split in 1997 in opposition the ceasefire declared by the Provisionals. The group is most known for the Omagh Bombing in 1998 and up to 2001 (our threshold for what counts as history here) had not carried out any major campaigns. The Real IRA can be identified by the style of Easter Lily pin (considerably more pronounced than what the PIRA is typically pictured with, if they are), and the uniforms (the cloth face mask/scarf with sunglasses and a beret is a classic Real IRA style).

Unlike previous IRA groups which focused on forcing the British out of Northern Ireland by means of a military-insurgent campaign focused on the island of Ireland, the Real IRA focused its earliest armed struggle activity on targets on the British mainland.

In terms of the actual footage - you won't find that easily precisely because of the illegal nature of these groups. There are general media blackouts on their announcements, meaning that there are no readily accessible online archives. This is partly a legacy of the broadcasting bans by the Irish and British states during the Troubles which (in Britain) prohibited any statements from paramilitary groups, and instead dubbed over them with voice actors, and (in Ireland) prohibited anything which could "that could be calculated to promote the aims or activities of any organisation which engages in, promotes, encourages or advocates the attaining of any particular objective by violent means". In 1976 this was extended to include all spokespeople for Sinn Féin and the IRA specifically, as opposed to being banned on the basis of the content. This ban was upheld for most of the conflict despite numerous court cases from Sinn Féin, journalists and trade unions attempting to get it overturned at both the Irish and European level.

The ban in Ireland fizzled out of existence into the 90s and before the Real IRA formed, but nonetheless when it came to more hardline dissident groups, the approach continued in practice, and some people were still officially banned as late as 1994. In addition, the British government lobbied online video hosters like YouTube to remove such videos from its service as they feared it would be used for Republican propaganda. This is what makes videos like this difficult to track down.

So, in terms of what was being announced in that video - I couldn't tell you. But the Real IRA in the 1997-2001 time period may have made five separate announcements:

1. Announcing their existence
2. Claiming responsibility for the Omagh Bombing
3. Declaring a ceasefire
4. Declaring the end of the ceasefire
5. Claiming responsibility for bombings in England

Generally, there are no "press conference" style announcements for claims of responsibility on attacks, so it is likely to be 1, 3 or 4.