Is this gramophone playing good?

You can see from the reflections on the rim of the records that they are "dished" i.e. not as flat as they should be. Maybe this is the fault of the mat the discs sit on but you can check the discs by putting them on a flat surface e.g. a  chess-board. It is also possible that the central holes are wider than they should be and so the discs are off-centered. A small thin sheet of tissue paper placed over the spindle before you place a disc might help. Don't force it,  find a thinner tissue if necessary. I notice that the stylus is possibly made of steel which gives a very bright even brittle sound and is the worst from the point of view of record wear.  However if you are only playing them once to make a recording that is not a problem. So the gramophone itself is probably OK. Record lovers of old would choose thorn styli and have cunning machines to resharpen them regularly but I doubt there are any suppliers nowadays. If I recall the styli were angled to point forward along the groove a little more than your picture shows.