Can video frame size be increased?
There are a few problems here that need to be addressed.  

First, the pitch shot is vertically oriented or "portrait" (vs landscape).  This is considered very, very bad practice.  This is a huge and constant amateur mistake because many amateurs now shoot video with their tablets and smartphones and hold the device the way they normally do, vertically, but this doesn't match up with the target format, which is generally either TV or even web video, which is generally displayed horizontally to make the most use of the space.

You should always shoot your video "landscape" or horizontal, just like you would see it on a TV so that it makes full use of the screen when being played back.  This orientation stems from the fact that we have a wider field of vision than we have tall, so a wide angle shot fill more of field of view and is more immersive.  A vertical or portrait shot does the opposite and doesn't fill well on a TV and barely scratches our field of view making it feel much less immersive.

The second major issue is that of video quality.  You can technically increase the number of pixels stored in the video by a process called upsampling or upscaling, but that doesn't increase the quality of your video (in fact, it generally decreases it further).  The easiest way to think about it is think about if you had 4 pixel image that had black square a white square and then on the next line a white square and a black square.

XO
OX


You can increase the number of pixels by duplicating what is there, but it doesn't invent more resolution (actual meaningful detail).  Say we scale it up to 9 by 9, you end up with this.

XXXXYOOOO
XXXXYOOOO
XXXXYOOOO
XXXXYOOOO
YYYYYYYYY
OOOOYXXXX
OOOOYXXXX
OOOOYXXXX
OOOOYXXXX


Note that there isn't any more detail than there was before, and we actually lost some detail because the new image had to invent pixels to fill where there are Ys because the original didn't evenly break up in to the new size, so it had to average the pixels that should have been there and made new grey Y pixels.  This means the image is now even less clear than it was before, when we had sharply defined squares because now we have fuzzy ones.

You could technically upscale to an exact multiple of your original to avoid interpolating, such as scaling up to 1428 by 1080 which will make the format meet the file format requirement technically, but it still won't meet it in spirit because the image will still be a 360p image (substantially lower than SD), rather than the requested 720P HD image requested.  Additionally, it would still be another encoding and thus another generation of compression loss to re-encode to the upscaled video, which would further sacrifice quality on your already abysmally low resolution video.

Third issue, though this one less major is that your aspect ratio is wrong.  This isn't necessarily a problem, but the formats they are recommending are widescreen formats.  Your current file is 4:3 rather than 16:9.  This may or may not be a problem for them.  Normally, if you have sufficient resolution and shot planning to do 16:9 it's pretty easy to crop down the video to a 16:9 form factor, but if you made full use of the vertical space in a way that you can't crop the top and/or bottom, then you are pretty much stuck at 4:3.  You also don't have enough resolution to start with to be able to sacrifice anything, which makes this a bigger concern.

Overall, my recommendation would be to re-shoot the pitch/interview portion using high resolution and proper orientation and aspect ratio.  For the existing video sample that you can't reshoot.  Submit it as is and hope for the best.  You can't meaningfully enhance it in a way that they are not going to see right through and probably dock you for trying to sneak around it.  Just explain the situation and why a higher quality version isn't available.  Either they'll go for it or they won't.  Nothing you artificially do is going to change that.